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Proof step 82 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), asynced ↔ false, dirs0[entries0[str]] = mkdir(m1, md3, # links(entries0[str], dirs0), m4, ∅), dirs0[m5] = mkdir(m0, md1, # links(m5, dirs0), m2, entries0), err = ESUCCESS, icache = icache0[inode.ino, mkientry(asynced, inode)], 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[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(icache0, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache0, pcache), entries0[str] ∈ dirs0, str ∈ entries0, m5 ∈ dirs0, 1 ≤ m2, 1 ≤ m0, asynced1 → synced(files, icache0, pcache), (m5 = entries0[str] ⊃ true;m0 ≥ 1 ∧ m2 ≥ 1), links(m5, dirs0) ≠ ∅ ∨ m5 = ROOT_INO ⊦ ⟪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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 83:
(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[m5] = mkdir(m0, md1, # links(m5, dirs0), m2, entries0), dirs0[entries0[str]] = mkdir(m1, md3, # links(entries0[str], dirs0), m4, ∅), err = ESUCCESS, icache = icache0 [entries0[str], mkientry (false, mkinode (entries0[str], md0, true, (entries0[str] = m5 ⊃ mkdir(m3, md, m7, m6, entries);mkdir(m3, md2, m7, m6, entries)).nlink, (entries0[str] = m5 ⊃ mkdir(m3, md, m7, m6, entries);mkdir(m3, md2, m7, m6, entries)).nsubdirs, (entries0[str] = m5 ⊃ mkdir(m3, md, m7, m6, entries);mkdir(m3, md2, m7, m6, entries)).size)) ], entries0[str] ≠ ROOT_INO, m0 ≠ 0, m2 ≠ 0, 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(icache0, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache0, pcache), m5 ∈ dirs0, str ∈ entries0, entries0[str] ∈ dirs0, 1 ≤ m0, 1 ≤ m2, asynced1 → synced(files, icache0, pcache), links(m5, dirs0) ≠ ∅ ∨ m5 = ROOT_INO ⊦ ⟪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:= md0 ] [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:= md0 ] [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:= md0 ] [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:= md0 ] [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)))

Rule argument

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)% ⊦ (ad.meta:= md).size = ad.size; (s)% ⊦ (ad.meta:= md).nsubdirs = ad.nsubdirs; (s)% ⊦ (ad.meta:= md).nlink = ad.nlink; (s)% ⊦ (ad.meta:= md).meta = md; (s)%⊦ getinode(ino, dirs, files) = (ino ∈ dirs ⊃ mkinode (ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ); (s)%⊦ mkdir(m, md, m0, m1, entries).meta:= md0 = mkdir(m, md0, m0, m1, entries); (s)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)