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Proof step 77 from proof inv-rmdir (previous step)

(entries0[str] = m ⊃ mkdir(m0 - 1, md1, # links(entries0[str], dirs0), m2 - 1, entries0 -- str) ;mkdir(m1, md3, # links(entries0[str], dirs0), m4, ∅) ) = mkdir(m3, md2, m5, m6, entries), dirs0[entries0[str]] = mkdir(m1, md3, # links(entries0[str], dirs0), m4, ∅), dirs0[m] = mkdir(m0, md1, # links(m, dirs0), m2, entries0), err = ESUCCESS, m5 = m7 + 1, afs-cons (dirs0[m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], (entries0[str] = m ⊃ mkdir(m3, md, m7, m6, entries);mkdir(m3, md2, m7, m6, entries)).meta:= md0 ], files), afs-cons(dirs0, files), dcache-cons(dcache, dirs0, files), icache-cons(icache, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache, pcache), entries0[str] ∈ dirs0, str ∈ entries0, m ∈ dirs0, 1 ≤ m5, 1 ≤ m2, 1 ≤ m0, asynced1 → synced(files, icache, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪icache_set# (getinode (entries0[str], dirs0[m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], dirs0[entries0[str], mkdir(m3, md2, m7, m6, entries)] [m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= md0 ], files), false ; err, icache); icache_set# (( m ∈ dirs0[m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], dirs0[entries0[str], mkdir(m3, md2, m7, m6, entries)] [m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= mkinode(entries0[str], md0, true, # links(entries0[str], dirs0), m4, m1).meta ] ⊃ mkinode (m, dirs0[m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], dirs0[entries0[str], mkdir(m3, md2, m7, m6, entries)] [m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= mkinode(entries0[str], md0, true, # links(entries0[str], dirs0), m4, m1).meta ] [m ] .meta, true, dirs0[m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], dirs0[entries0[str], mkdir(m3, md2, m7, m6, entries)] [m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= mkinode(entries0[str], md0, true, # links(entries0[str], dirs0), m4, m1).meta ] [m ] .nlink, dirs0[m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], dirs0[entries0[str], mkdir(m3, md2, m7, m6, entries)] [m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= mkinode(entries0[str], md0, true, # links(entries0[str], dirs0), m4, m1).meta ] [m ] .nsubdirs, dirs0[m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], dirs0[entries0[str], mkdir(m3, md2, m7, m6, entries)] [m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= mkinode(entries0[str], md0, true, # links(entries0[str], dirs0), m4, m1).meta ] [m ] .size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ), false ; err, icache); dcache_delete# (( m ∈ dirs0[m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], dirs0[entries0[str], mkdir(m3, md2, m7, m6, entries)] [m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= mkinode(entries0[str], md0, true, # links(entries0[str], dirs0), m4, m1).meta ] ⊃ mkinode (m, dirs0[m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], dirs0[entries0[str], mkdir(m3, md2, m7, m6, entries)] [m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= mkinode(entries0[str], md0, true, # links(entries0[str], dirs0), m4, m1).meta ] [m ] .meta, true, dirs0[m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], dirs0[entries0[str], mkdir(m3, md2, m7, m6, entries)] [m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= mkinode(entries0[str], md0, true, # links(entries0[str], dirs0), m4, m1).meta ] [m ] .nlink, dirs0[m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], dirs0[entries0[str], mkdir(m3, md2, m7, m6, entries)] [m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= mkinode(entries0[str], md0, true, # links(entries0[str], dirs0), m4, m1).meta ] [m ] .nsubdirs, dirs0[m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], dirs0[entries0[str], mkdir(m3, md2, m7, m6, entries)] [m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= mkinode(entries0[str], md0, true, # links(entries0[str], dirs0), m4, m1).meta ] [m ] .size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ) .ino, mkdentry(str, entries0[str]).name ; err, dcache)⟫ ( icache-cons (icache, dirs0[m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], (entries0[str] = m ⊃ mkdir(m3, md, m7, m6, entries);mkdir(m3, md2, m7, m6, entries)).meta:= md0 ], files) ∧ dcache-cons (dcache, dirs0[m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], (entries0[str] = m ⊃ mkdir(m3, md, m7, m6, entries);mkdir(m3, md2, m7, m6, entries)).meta:= md0 ], files) ∧ pcache-cons (pcache, dirs0[m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], (entries0[str] = m ⊃ mkdir(m3, md, m7, m6, entries);mkdir(m3, md2, m7, m6, entries)).meta:= md0 ], files) ∧ synced (dirs0[m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], (entries0[str] = m ⊃ mkdir(m3, md, m7, m6, entries);mkdir(m3, md2, m7, m6, entries)).meta:= md0 ], icache, pcache) ∧ (asynced1 → synced(files, icache, pcache))), entries0[str] = ROOT_INO, m0 = 0, m2 = 0, m5 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 78:
(entries0[str] = m ⊃ mkdir(m0 - 1, md1, # links(entries0[str], dirs0), m2 - 1, entries0 -- str) ;mkdir(m1, md3, # links(entries0[str], dirs0), m4, ∅) ) = mkdir(m3, md2, m7 + 1, m6, entries), dirs0[m] = mkdir(m0, md1, # links(m, dirs0), m2, entries0), dirs0[entries0[str]] = mkdir(m1, md3, # links(entries0[str], dirs0), m4, ∅), err = ESUCCESS, entries0[str] ≠ ROOT_INO, m0 ≠ 0, m2 ≠ 0, afs-cons(dirs0, files), afs-cons (dirs0[m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], (entries0[str] = m ⊃ mkdir(m3, md, m7, m6, entries);mkdir(m3, md2, m7, m6, entries)).meta:= md0 ], files), dcache-cons(dcache, dirs0, files), icache-cons(icache, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache, pcache), m ∈ dirs0, str ∈ entries0, entries0[str] ∈ dirs0, 1 ≤ m0, 1 ≤ m2, asynced1 → synced(files, icache, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪icache_set# (getinode (entries0[str], dirs0[m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], dirs0[entries0[str], mkdir(m3, md2, m7, m6, entries)] [m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= md0 ], files), false ; err, icache); icache_set# ((m ∈ dirs0[m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md] ⊃ mkinode (m, dirs0[m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], dirs0[entries0[str], mkdir(m3, md2, m7, m6, entries)] [m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= mkinode(entries0[str], md0, true, # links(entries0[str], dirs0), m4, m1).meta ] [m ] .meta, true, dirs0[m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], dirs0[entries0[str], mkdir(m3, md2, m7, m6, entries)] [m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= mkinode(entries0[str], md0, true, # links(entries0[str], dirs0), m4, m1).meta ] [m ] .nlink, dirs0[m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], dirs0[entries0[str], mkdir(m3, md2, m7, m6, entries)] [m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= mkinode(entries0[str], md0, true, # links(entries0[str], dirs0), m4, m1).meta ] [m ] .nsubdirs, dirs0[m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], dirs0[entries0[str], mkdir(m3, md2, m7, m6, entries)] [m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= mkinode(entries0[str], md0, true, # links(entries0[str], dirs0), m4, m1).meta ] [m ] .size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ), false ; err, icache); dcache_delete# ((m ∈ dirs0[m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md] ⊃ mkinode (m, dirs0[m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], dirs0[entries0[str], mkdir(m3, md2, m7, m6, entries)] [m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= mkinode(entries0[str], md0, true, # links(entries0[str], dirs0), m4, m1).meta ] [m ] .meta, true, dirs0[m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], dirs0[entries0[str], mkdir(m3, md2, m7, m6, entries)] [m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= mkinode(entries0[str], md0, true, # links(entries0[str], dirs0), m4, m1).meta ] [m ] .nlink, dirs0[m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], dirs0[entries0[str], mkdir(m3, md2, m7, m6, entries)] [m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= mkinode(entries0[str], md0, true, # links(entries0[str], dirs0), m4, m1).meta ] [m ] .nsubdirs, dirs0[m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], dirs0[entries0[str], mkdir(m3, md2, m7, m6, entries)] [m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= mkinode(entries0[str], md0, true, # links(entries0[str], dirs0), m4, m1).meta ] [m ] .size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ) .ino, mkdentry(str, entries0[str]).name ; err, dcache)⟫ ( icache-cons (icache, dirs0[m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], (entries0[str] = m ⊃ mkdir(m3, md, m7, m6, entries);mkdir(m3, md2, m7, m6, entries)).meta:= md0 ], files) ∧ dcache-cons (dcache, dirs0[m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], (entries0[str] = m ⊃ mkdir(m3, md, m7, m6, entries);mkdir(m3, md2, m7, m6, entries)).meta:= md0 ], files) ∧ pcache-cons (pcache, dirs0[m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], (entries0[str] = m ⊃ mkdir(m3, md, m7, m6, entries);mkdir(m3, md2, m7, m6, entries)).meta:= md0 ], files) ∧ synced (dirs0[m, (m = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], (entries0[str] = m ⊃ mkdir(m3, md, m7, m6, entries);mkdir(m3, md2, m7, m6, entries)).meta:= md0 ], icache, pcache) ∧ (asynced1 → synced(files, icache, pcache)))

Rule argument

Additional information

Used simplifier rules: ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)% ⊦ m ≤ m + n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≠ 0; (s)