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

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Proof step 132 from proof inv-rename-file-dentry (previous step)

# links(entries1[str], dirs0) = m11 + 1, (m = m0 ⊃ mkdir(m1, md6, # links(m0, dirs0), m7, entries -- str0);mkdir(m4, md4, # links(m, dirs0), m8, entries1)) = mkdir(m6, md3, m9, m10, entries0), asynced ↔ false, dirs0[m0] = mkdir(m1 + 1, md6, # links(m0, dirs0), m7, entries), files0[entries[str0]] = mkfile(m3, md0, # links(entries[str0], dirs0), content), files0[entries1[str]] = mkfile(m5, md5, m11 + 1, content1), dirs0[m] = mkdir(m4, md4, # links(m, dirs0), m8, entries1), err = ESUCCESS, icache = icache0[inode.ino, mkientry(asynced, inode)], inode = ( m0 ∈ dirs0 [m0, (m0 = m ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m0, dirs0), m7, entries -- str0)).meta:= md2 ] ⊃ mkinode (m0, dirs0 [m0, (m0 = m ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m0, dirs0), m7, entries -- str0)).meta:= md2 ] [m, (m = m0 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).meta:= md1 ] [m0 ] .meta, true, dirs0 [m0, (m0 = m ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m0, dirs0), m7, entries -- str0)).meta:= md2 ] [m, (m = m0 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).meta:= md1 ] [m0 ] .nlink, dirs0 [m0, (m0 = m ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m0, dirs0), m7, entries -- str0)).meta:= md2 ] [m, (m = m0 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).meta:= md1 ] [m0 ] .nsubdirs, dirs0 [m0, (m0 = m ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m0, dirs0), m7, entries -- str0)).meta:= md2 ] [m, (m = m0 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).meta:= md1 ] [m0 ] .size) ;mkinode (m0, files0 [entries1[str], files0[entries1[str], files0[entries1[str], mkfile(m5, md5, m11, content1)][entries1[str]].size:= m2][entries1[str]].meta:= md ] [m0 ] .meta, false, files0 [entries1[str], files0[entries1[str], files0[entries1[str], mkfile(m5, md5, m11, content1)][entries1[str]].size:= m2][entries1[str]].meta:= md ] [m0 ] .nlink, 0, files0 [entries1[str], files0[entries1[str], files0[entries1[str], mkfile(m5, md5, m11, content1)][entries1[str]].size:= m2][entries1[str]].meta:= md ] [m0 ] .size) ), afs-cons(dirs0, files0), afs-cons (dirs0[m0, (m0 = m ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m0, dirs0), m7, entries -- str0)).meta:= md2] [m, (m = m0 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).meta:= md1 ], files0[entries1[str], mkfile(m2, md, m11, content1)]), dcache-cons(dcache, dirs0, files0), icache-cons(icache0, dirs0, files0), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache0, pcache), str0 ∈ entries, entries[str0] ∈ files0, m0 ∈ dirs0, str ∈ entries1, m ∈ dirs0, entries1[str] ∈ files0, m = m0 → md1 = md2, asynced2 → synced(files0, icache0, pcache), ( m0 ∈ dirs0[m0, (m0 = m ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m0, dirs0), m7, entries -- str0)).meta:= md2] ⊃ ((m0 = m ⊃ str0 ∈ entries;true) ∧ str0 ∈ entries) ∧ ((m0 = m ⊃ str0 ∈ entries;true) ∧ str0 ∈ entries) ∧ ((m0 = m ⊃ str0 ∈ entries;true) ∧ str0 ∈ entries) ∧ (m0 = m ⊃ str0 ∈ entries;true) ∧ str0 ∈ entries ; (str ∈ entries1 ∧ (str ∈ entries1 ∧ str ∈ entries1 ∧ str ∈ entries1) ∧ str ∈ entries1) ∧ (str ∈ entries1 ∧ (str ∈ entries1 ∧ str ∈ entries1 ∧ str ∈ entries1) ∧ str ∈ entries1) ∧ str ∈ entries1 ∧ (str ∈ entries1 ∧ str ∈ entries1 ∧ str ∈ entries1) ∧ str ∈ entries1 ), (m0 = m ⊃ str0 ∈ entries;true), links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪icache_set# (( m ∈ dirs0 [m0, (m0 = m ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m0, dirs0), m7, entries -- str0)).meta:= md2 ] [m, (m = m0 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).meta:= md1 ] ⊃ mkinode (m, dirs0 [m0, (m0 = m ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m0, dirs0), m7, entries -- str0)).meta:= md2 ] [m, (m = m0 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).meta:= md1 ] [m ] .meta, true, dirs0 [m0, (m0 = m ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m0, dirs0), m7, entries -- str0)).meta:= md2 ] [m, (m = m0 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).meta:= md1 ] [m ] .nlink, dirs0 [m0, (m0 = m ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m0, dirs0), m7, entries -- str0)).meta:= md2 ] [m, (m = m0 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).meta:= md1 ] [m ] .nsubdirs, dirs0 [m0, (m0 = m ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m0, dirs0), m7, entries -- str0)).meta:= md2 ] [m, (m = m0 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).meta:= md1 ] [m ] .size) ;mkinode (m, files0 [entries1[str], files0 [entries1[str], files0[entries1[str], mkfile(m5, md5, m11, content1)][entries1[str]] .size:= mkinode(entries1[str], md, false, # links(entries1[str], dirs0), 0, m2).size ] [entries1[str] ] .meta:= mkinode(entries1[str], md, false, # links(entries1[str], dirs0), 0, m2).meta ] [m ] .meta, false, files0 [entries1[str], files0 [entries1[str], files0[entries1[str], mkfile(m5, md5, m11, content1)][entries1[str]] .size:= mkinode(entries1[str], md, false, # links(entries1[str], dirs0), 0, m2).size ] [entries1[str] ] .meta:= mkinode(entries1[str], md, false, # links(entries1[str], dirs0), 0, m2).meta ] [m ] .nlink, 0, files0 [entries1[str], files0 [entries1[str], files0[entries1[str], mkfile(m5, md5, m11, content1)][entries1[str]] .size:= mkinode(entries1[str], md, false, # links(entries1[str], dirs0), 0, m2).size ] [entries1[str] ] .meta:= mkinode(entries1[str], md, false, # links(entries1[str], dirs0), 0, m2).meta ] [m ] .size) ), false ; err, icache); inode := mkinode(entries1[str], md, false, # links(entries1[str], dirs0), 0, m2); ino := entries1[str]; files := files0[entries1[str], mkfile(m5, md5, m11, content1)]; dirs := dirs0 [m0, (m0 = m ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m0, dirs0), m7, entries -- str0)).meta:= md2 ] [m, (m = m0 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).meta:= md1 ]; icache_set# ((entries1[str] ∈ dirs ⊃ mkinode(entries1[str], dirs[entries1[str]].meta, true, dirs[entries1[str]].nlink, dirs[entries1[str]].nsubdirs, dirs[entries1[str]].size) ;mkinode (entries1[str], files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta][entries1[str]].meta, false, files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta][entries1[str]].nlink, 0, files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta][entries1[str]].size) ), false ; err, icache); dcache_delete# ((m0 ∈ dirs ⊃ mkinode(m0, dirs[m0].meta, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size) ;mkinode (m0, (m0 = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.meta;files[m0]).meta, false, (m0 = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.meta;files[m0]).nlink, 0, (m0 = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.meta;files[m0]).size) ) .ino, mkdentry(str0, entries[str0]).name ; err, dcache); dcache_set# ((m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode (m, (m = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.meta;files[m]).meta, false, (m = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.meta;files[m]).nlink, 0, (m = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.meta;files[m]).size) ) .ino, mkdentry(mkdentry(str, entries1[str]).name, mkdentry(str0, entries[str0]).ino).name, mkdentry(mkdentry(str, entries1[str]).name, mkdentry(str0, entries[str0]).ino) ; err, dcache)⟫ ( icache-cons(icache, dirs, files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta]) ∧ dcache-cons(dcache, dirs, files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta]) ∧ pcache-cons(pcache, dirs, files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta]) ∧ synced(dirs, icache, pcache) ∧ (asynced2 → synced(files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta], icache, pcache))), entries1[str] ∈ dirs0, entries[str0] ∈ dirs0, m0 = m ∧ mkdentry(str, entries1[str]) = mkdentry(str0, entries[str0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 133:
# links(entries1[str], dirs0) = m11 + 1, (m = m0 ⊃ mkdir(m1, md6, # links(m0, dirs0), m7, entries -- str0);mkdir(m4, md4, # links(m, dirs0), m8, entries1)) = mkdir(m6, md3, m9, m10, entries0), dirs0[m] = mkdir(m4, md4, # links(m, dirs0), m8, entries1), files0[entries1[str]] = mkfile(m5, md5, m11 + 1, content1), files0[entries[str0]] = mkfile(m3, md0, # links(entries[str0], dirs0), content), dirs0[m0] = mkdir(m1 + 1, md6, # links(m0, dirs0), m7, entries), err = ESUCCESS, icache = icache0 [m0, mkientry (false, mkinode (m0, (m0 = m ⊃ mkdir(m6, md1, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md2, # links(m0, dirs0), m7, entries -- str0)).meta, true, (m0 = m ⊃ mkdir(m6, md1, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md2, # links(m0, dirs0), m7, entries -- str0)).nlink, (m0 = m ⊃ mkdir(m6, md1, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md2, # links(m0, dirs0), m7, entries -- str0)).nsubdirs, (m0 = m ⊃ mkdir(m6, md1, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md2, # links(m0, dirs0), m7, entries -- str0)).size)) ], afs-cons (dirs0[m0, (m0 = m ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m0, dirs0), m7, entries -- str0)).meta:= md2] [m, (m = m0 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).meta:= md1 ], files0[entries1[str], mkfile(m2, md, m11, content1)]), afs-cons(dirs0, files0), dcache-cons(dcache, dirs0, files0), icache-cons(icache0, dirs0, files0), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache0, pcache), entries1[str] ∈ files0, m ∈ dirs0, str ∈ entries1, m0 ∈ dirs0, entries[str0] ∈ files0, str0 ∈ entries, ¬ entries[str0] ∈ dirs0, ¬ entries1[str] ∈ dirs0, asynced2 → synced(files0, icache0, pcache), m = m0 → md1 = md2, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ⟪icache_set# (( m ∈ dirs0 [m0, (m0 = m ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m0, dirs0), m7, entries -- str0)).meta:= md2 ] ⊃ mkinode (m, dirs0 [m0, (m0 = m ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m0, dirs0), m7, entries -- str0)).meta:= md2 ] [m, (m = m0 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).meta:= md1 ] [m ] .meta, true, dirs0 [m0, (m0 = m ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m0, dirs0), m7, entries -- str0)).meta:= md2 ] [m, (m = m0 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).meta:= md1 ] [m ] .nlink, dirs0 [m0, (m0 = m ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m0, dirs0), m7, entries -- str0)).meta:= md2 ] [m, (m = m0 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).meta:= md1 ] [m ] .nsubdirs, dirs0 [m0, (m0 = m ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m0, dirs0), m7, entries -- str0)).meta:= md2 ] [m, (m = m0 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).meta:= md1 ] [m ] .size) ;mkinode (m, files0 [entries1[str], files0[entries1[str], files0[entries1[str], mkfile(m5, md5, m11, content1)][entries1[str]].size:= m2][entries1[str]].meta:= md ] [m ] .meta, false, files0 [entries1[str], files0[entries1[str], files0[entries1[str], mkfile(m5, md5, m11, content1)][entries1[str]].size:= m2][entries1[str]].meta:= md ] [m ] .nlink, 0, files0 [entries1[str], files0[entries1[str], files0[entries1[str], mkfile(m5, md5, m11, content1)][entries1[str]].size:= m2][entries1[str]].meta:= md ] [m ] .size) ), false ; err, icache); inode := mkinode(entries1[str], md, false, # links(entries1[str], dirs0), 0, m2); ino := entries1[str]; files := files0[entries1[str], mkfile(m5, md5, m11, content1)]; dirs := dirs0 [m0, (m0 = m ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m0, dirs0), m7, entries -- str0)).meta:= md2 ] [m, (m = m0 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).meta:= md1 ]; icache_set# ((entries1[str] ∈ dirs ⊃ mkinode(entries1[str], dirs[entries1[str]].meta, true, dirs[entries1[str]].nlink, dirs[entries1[str]].nsubdirs, dirs[entries1[str]].size) ;mkinode (entries1[str], files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta][entries1[str]].meta, false, files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta][entries1[str]].nlink, 0, files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta][entries1[str]].size) ), false ; err, icache); dcache_delete# ((m0 ∈ dirs ⊃ mkinode(m0, dirs[m0].meta, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size) ;mkinode (m0, (m0 = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.meta;files[m0]).meta, false, (m0 = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.meta;files[m0]).nlink, 0, (m0 = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.meta;files[m0]).size) ) .ino, mkdentry(str0, entries[str0]).name ; err, dcache); dcache_set# ((m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode (m, (m = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.meta;files[m]).meta, false, (m = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.meta;files[m]).nlink, 0, (m = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.meta;files[m]).size) ) .ino, mkdentry(mkdentry(str, entries1[str]).name, mkdentry(str0, entries[str0]).ino).name, mkdentry(mkdentry(str, entries1[str]).name, mkdentry(str0, entries[str0]).ino) ; err, dcache)⟫ ( icache-cons(icache, dirs, files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta]) ∧ dcache-cons(dcache, dirs, files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta]) ∧ pcache-cons(pcache, dirs, files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta]) ∧ synced(dirs, icache, pcache) ∧ (asynced2 → synced(files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta], icache, pcache))), m0 = m ∧ mkdentry(str, entries1[str]) = mkdentry(str0, entries[str0])

Rule argument

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (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)