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Proof step 101 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), asynced ↔ false, 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), dirs = 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 ], err = ESUCCESS, ino = inode.ino, inode = mkinode(m0, md1, true, # links(m0, dirs0), m10, m8), afs-cons(dirs0, files), afs-cons(dirs[ino, dirs[ino].meta:= inode.meta], 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, ino ∈ dirs, asynced2 → synced(files, icache, pcache), m0 = m → md1 = md0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ⟪icache_set# ((m ∈ dirs[ino, dirs[ino].meta:= inode.meta] ⊃ mkinode (m, dirs[ino, dirs[ino].meta:= inode.meta][m].meta, true, dirs[ino, dirs[ino].meta:= inode.meta][m].nlink, dirs[ino, dirs[ino].meta:= inode.meta][m].nsubdirs, dirs[ino, dirs[ino].meta:= inode.meta][m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ), asynced ; err, icache); icache_set# ((m0 ∈ dirs[ino, dirs[ino].meta:= inode.meta] ⊃ mkinode (m0, dirs[ino, dirs[ino].meta:= inode.meta][m0].meta, true, dirs[ino, dirs[ino].meta:= inode.meta][m0].nlink, dirs[ino, dirs[ino].meta:= inode.meta][m0].nsubdirs, dirs[ino, dirs[ino].meta:= inode.meta][m0].size) ;mkinode(m0, files[m0].meta, false, files[m0].nlink, 0, files[m0].size) ), asynced ; err, icache); skip; dcache_delete# ((m ∈ dirs[ino, dirs[ino].meta:= inode.meta] ⊃ mkinode (m, dirs[ino, dirs[ino].meta:= inode.meta][m].meta, true, dirs[ino, dirs[ino].meta:= inode.meta][m].nlink, dirs[ino, dirs[ino].meta:= inode.meta][m].nsubdirs, dirs[ino, dirs[ino].meta:= inode.meta][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 ∈ dirs[ino, dirs[ino].meta:= inode.meta] ⊃ mkinode (m0, dirs[ino, dirs[ino].meta:= inode.meta][m0].meta, true, dirs[ino, dirs[ino].meta:= inode.meta][m0].nlink, dirs[ino, dirs[ino].meta:= inode.meta][m0].nsubdirs, dirs[ino, dirs[ino].meta:= inode.meta][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, dirs[ino, dirs[ino].meta:= inode.meta], files) ∧ dcache-cons(dcache, dirs[ino, dirs[ino].meta:= inode.meta], files) ∧ pcache-cons(pcache, dirs[ino, dirs[ino].meta:= inode.meta], files) ∧ synced(dirs[ino, dirs[ino].meta:= inode.meta], icache, pcache) ∧ (asynced2 → synced(files, icache, pcache))), str0 ∈ entries3, ino ∈ files

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 102:
(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)))

Rule argument

Additional information

Used simplifier rules: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)% ⊦ dirs[ino, ad][ino0, ad0][ino, ad1] = dirs[ino0, ad0][ino, ad1]; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)%⊦ mkdir(m, md, m0, m1, entries).meta:= md0 = mkdir(m, md0, m0, m1, entries); (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)