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Proof step 80 from proof inv-rmdir (previous step)

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

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 81:
(entries0[str] = m5 ⊃ 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), asynced ↔ false, dirs0[m5] = mkdir(m0, md1, # links(m5, dirs0), m2, entries0), dirs0[entries0[str]] = mkdir(m1, md3, # links(entries0[str], dirs0), m4, ∅), err = ESUCCESS, inode = getinode (entries0[str], dirs0[m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], dirs0[entries0[str], mkdir(m3, md2, m7, m6, entries)] [m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= md0 ], files), afs-cons(dirs0, files), afs-cons (dirs0[m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], (entries0[str] = m5 ⊃ 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), m5 ∈ dirs0, str ∈ entries0, entries0[str] ∈ dirs0, 1 ≤ m0, 1 ≤ m2, asynced1 → synced(files, icache, pcache), (m5 = entries0[str] ⊃ true;m0 ≥ 1 ∧ m2 ≥ 1), links(m5, dirs0) ≠ ∅ ∨ m5 = ROOT_INO ⊦ ⟪icache[inode.ino] := mkientry(asynced, inode); icache_set# (( m5 ∈ dirs0[m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md] ⊃ mkinode (m5, dirs0[m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], dirs0[entries0[str], mkdir(m3, md2, m7, m6, entries)] [m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= mkinode(entries0[str], md0, true, # links(entries0[str], dirs0), m4, m1).meta ] [m5 ] .meta, true, dirs0[m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], dirs0[entries0[str], mkdir(m3, md2, m7, m6, entries)] [m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= mkinode(entries0[str], md0, true, # links(entries0[str], dirs0), m4, m1).meta ] [m5 ] .nlink, dirs0[m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], dirs0[entries0[str], mkdir(m3, md2, m7, m6, entries)] [m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= mkinode(entries0[str], md0, true, # links(entries0[str], dirs0), m4, m1).meta ] [m5 ] .nsubdirs, dirs0[m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], dirs0[entries0[str], mkdir(m3, md2, m7, m6, entries)] [m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= mkinode(entries0[str], md0, true, # links(entries0[str], dirs0), m4, m1).meta ] [m5 ] .size) ;mkinode(m5, files[m5].meta, false, files[m5].nlink, 0, files[m5].size) ), false ; err, icache); dcache_delete#(m5, mkdentry(str, entries0[str]).name; err, dcache)⟫ ( icache-cons (icache, dirs0 [m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str], (entries0[str] = m5 ⊃ mkdir(m3, md, m7, m6, entries);mkdir(m3, md2, m7, m6, entries)).meta:= md0 ], files) ∧ dcache-cons (dcache, dirs0 [m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str], (entries0[str] = m5 ⊃ mkdir(m3, md, m7, m6, entries);mkdir(m3, md2, m7, m6, entries)).meta:= md0 ], files) ∧ pcache-cons (pcache, dirs0 [m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str], (entries0[str] = m5 ⊃ mkdir(m3, md, m7, m6, entries);mkdir(m3, md2, m7, m6, entries)).meta:= md0 ], files) ∧ synced (dirs0 [m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str], (entries0[str] = m5 ⊃ 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

Rule argument

pos: right 1

Additional information

Used simplifier rules: icache_set#(INODE, DIRTY; ERR, ICACHE) {ICACHE[INODE.ino] := mkientry(DIRTY, INODE)};% ⊦ n ≥ m ↔ m ≤ n; (s)