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

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

asynced ↔ false, dirs0[ino1] = mkdir(m5, md2, # links(ino1, dirs0), m10, entries1), entries[str] = entries2[str], dirs0[ino0] = mkdir(m2, md1, # links(ino0, dirs0), m8, entries), entries0[str] = entries2[str], files0[entries2[str]] = mkfile(m0, md6, # links(entries2[str], dirs0), content0), dirs0[m] = mkdir(m1, md5, # links(m, dirs0), m9, entries3), dirs0[ino2] = mkdir(m4, md3, # links(ino2, dirs0), m6, entries0), entries1[str] = entries2[str], dirs0[ino3] = mkdir(m7, md4, # links(ino3, dirs0), m12, entries2), dirs = dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])], err = ESUCCESS, files = files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)], ino = inode.ino, inode = mkinode(entries1[str], md0, false, # links(entries1[str], dirs0), 0, m3), mkdentry(str, entries0[str]).dentry?, afs-cons(dirs0, files0), afs-cons(dirs, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta]), dcache-cons(dcache, dirs0, files0), icache-cons(icache, dirs0, files0), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache, pcache), str ∈ entries1, ino1 ∈ dirs0, str ∈ entries, ino0 ∈ dirs0, ino2 ∈ dirs0, str ∈ entries0, entries2[str] ∈ files0, ino3 ∈ dirs0, str ∈ entries2, m ∈ dirs0, ino ∈ files, asynced1 → synced(files0, icache, pcache), links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO, links(ino0, dirs0) ≠ ∅ ∨ ino0 = ROOT_INO, links(ino2, dirs0) ≠ ∅ ∨ ino2 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(ino3, dirs0) ≠ ∅ ∨ ino3 = ROOT_INO ⊦ ⟪icache_set# ((m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode (m, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta][m].meta, false, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta][m].nlink, 0, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta][m].size) ), asynced ; err, icache); icache_set# (getinode (mkdentry(str, entries0[str]).ino, dirs, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta]), asynced ; err, icache); dcache_set# ((m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode (m, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta][m].meta, false, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta][m].nlink, 0, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta][m].size) ) .ino, mkdentry(str0, mkdentry(str, entries0[str]).ino).name, mkdentry(str0, mkdentry(str, entries0[str]).ino) ; err, dcache)⟫ ( icache-cons(icache, dirs, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta]) ∧ dcache-cons(dcache, dirs, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta]) ∧ pcache-cons(pcache, dirs, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta]) ∧ synced(dirs, icache, pcache) ∧ ( asynced1 → synced(files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta], icache, pcache))), str0 ∈ entries3

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 81:
dirs0[ino1] = mkdir(m5, md2, # links(ino1, dirs0), m10, entries1), entries[str] = entries2[str], dirs0[ino0] = mkdir(m2, md1, # links(ino0, dirs0), m8, entries), entries0[str] = entries2[str], files0[entries2[str]] = mkfile(m0, md6, # links(entries2[str], dirs0), content0), dirs0[m] = mkdir(m1, md5, # links(m, dirs0), m9, entries3), dirs0[ino2] = mkdir(m4, md3, # links(ino2, dirs0), m6, entries0), entries1[str] = entries2[str], dirs0[ino3] = mkdir(m7, md4, # links(ino3, dirs0), m12, entries2), err = ESUCCESS, afs-cons(dirs0, files0), afs-cons (dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])], files0[entries2[str], mkfile(m3, md0, # links(entries2[str], dirs0) + 1, content0)]), dcache-cons(dcache, dirs0, files0), icache-cons(icache, dirs0, files0), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache, pcache), str ∈ entries1, ino1 ∈ dirs0, str ∈ entries, ino0 ∈ dirs0, ino2 ∈ dirs0, str ∈ entries0, ino3 ∈ dirs0, str ∈ entries2, m ∈ dirs0, entries2[str] ∈ files0, ¬ str0 ∈ entries3, asynced1 → synced(files0, icache, pcache), links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO, links(ino0, dirs0) ≠ ∅ ∨ ino0 = ROOT_INO, links(ino2, dirs0) ≠ ∅ ∨ ino2 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(ino3, dirs0) ≠ ∅ ∨ ino3 = ROOT_INO ⊦ ⟪icache_set# (mkinode (m, dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])][m].meta, true, dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])][m].nlink, dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])][m].nsubdirs, dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])][m].size), false ; err, icache); icache_set# (getinode (mkdentry(str, entries0[str]).ino, dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)][entries1[str]] .size:= mkinode(entries1[str], md0, false, # links(entries1[str], dirs0), 0, m3).size ] [entries1[str] ] .meta:= mkinode(entries1[str], md0, false, # links(entries1[str], dirs0), 0, m3).meta ]), false ; err, icache); dcache_set# ((m ∈ dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])] ⊃ mkinode (m, dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])][m].meta, true, dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])][m].nlink, dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])][m].nsubdirs, dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])][m].size) ;mkinode (m, files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)][entries1[str]] .size:= mkinode(entries1[str], md0, false, # links(entries1[str], dirs0), 0, m3).size ] [entries1[str] ] .meta:= mkinode(entries1[str], md0, false, # links(entries1[str], dirs0), 0, m3).meta ] [m ] .meta, false, files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)][entries1[str]] .size:= mkinode(entries1[str], md0, false, # links(entries1[str], dirs0), 0, m3).size ] [entries1[str] ] .meta:= mkinode(entries1[str], md0, false, # links(entries1[str], dirs0), 0, m3).meta ] [m ] .nlink, 0, files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)][entries1[str]] .size:= mkinode(entries1[str], md0, false, # links(entries1[str], dirs0), 0, m3).size ] [entries1[str] ] .meta:= mkinode(entries1[str], md0, false, # links(entries1[str], dirs0), 0, m3).meta ] [m ] .size) ) .ino, mkdentry(str0, mkdentry(str, entries0[str]).ino).name, mkdentry(str0, mkdentry(str, entries0[str]).ino) ; err, dcache)⟫ ( icache-cons (icache, dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], mkfile(m3, md0, # links(entries2[str], dirs0) + 1, content0) ]) ∧ dcache-cons (dcache, dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], mkfile(m3, md0, # links(entries2[str], dirs0) + 1, content0) ]) ∧ pcache-cons (pcache, dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], mkfile(m3, md0, # links(entries2[str], dirs0) + 1, content0) ]) ∧ synced(dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])], icache, pcache) ∧ ( asynced1 → synced (files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], mkfile(m3, md0, # links(entries2[str], dirs0) + 1, content0) ], icache, pcache)))

Rule argument

Additional information

Used simplifier rules: ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)% ⊦ mkdentry(str, m).dentry?; (s)% ⊦ files[ino, af][ino, af0] = files[ino, af0]; (s)% ⊦ mkfile(m, md, m0, content).meta:= md0 = mkfile(m, md0, m0, content); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ mkfile(m, md, m0, content).size:= m1 = mkfile(m1, md, m0, content); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)