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

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 128 from proof refine-link (previous step)

fs0[ri0[dentrykey(ino1, str)]].ino = fs0[ri0[dentrykey(ino3, str)]].ino, fs0[ri0[dentrykey(ino2, str)]] = dentrynode(key3, fs0[ri0[dentrykey(ino3, str)]].ino), fs0[ri0[inodekey(fs0[ri0[dentrykey(ino3, str)]].ino)]] = inodenode(key1, md2, false, m3, 0, m5), fs0[ri0[dentrykey(ino4, str)]] = dentrynode(key, fs0[ri0[dentrykey(ino3, str)]].ino), fs0[ri0[inodekey(m)]] = inodenode(key0, md1, true, m0, m1, m2), fs0[ri0[dentrykey(ino0, str)]] = dentrynode(key2, fs0[ri0[dentrykey(ino3, str)]].ino), dirs = dirs0[ino, dirs0[ino].meta:= inode.meta], dirs0 = abs-dirs(fs0, ri0)[m, mkdir(m2 + 1, md1, m0, m1, abs-children(m, fs0, ri0)[str0, fs0[ri0[dentrykey(ino3, str)]].ino])], files = abs-files(fs0, ri0)[fs0[ri0[dentrykey(ino3, str)]].ino, mkfile(m5, md2, m3 + 1, abs-content(fs0[ri0[dentrykey(ino3, str)]].ino, fs0, ri0))], ino = inode.ino, inode = mkinode(m, md, true, m0, m1, m2), fs0[ri0[inodekey(ino2)]].directory, fs0[ri0[inodekey(ino0)]].directory, fs0[ri0[inodekey(ino1)]].directory, fs0[ri0[inodekey(ino4)]].directory, fs0[ri0[inodekey(ino3)]].directory, fo.inodes?, orphans(fs0, ri0).inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino3, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino3, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino3, str)]].ino), adr3]), file-node-cons(fs0, ri0), log-cons (log0, fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino3, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino3, str)]].ino), md0, false, m3 + 1, 0, m6) ]), log-cons(log0, fs0), orphans-cons (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino3, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino3, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino3, str)]].ino), adr3], orphans(fs0, ri0)), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino3, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino3, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino3, str)]].ino), adr3], orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri-cons(ri0, fs0), ri-inj(ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino3, str)]].ino), adr3]), ri-inj(fi), ri-inj(ri0), ubifs-cons (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino3, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino3, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino3, str)]].ino), adr3], orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), inodekey(ino0) ∈ ri0, dentrykey(ino0, str) ∈ ri0, ri0[dentrykey(ino0, str)] ∈ fs0, dentrykey(ino2, str) ∈ ri0, inodekey(ino2) ∈ ri0, dentrykey(ino4, str) ∈ ri0, ri0[dentrykey(ino4, str)] ∈ fs0, inodekey(fs0[ri0[dentrykey(ino3, str)]].ino) ∈ ri0, ri0[inodekey(fs0[ri0[dentrykey(ino3, str)]].ino)] ∈ fs0, dentrykey(ino1, str) ∈ ri0, inodekey(ino1) ∈ ri0, ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, inodekey(ino3) ∈ ri0, dentrykey(ino3, str) ∈ ri0, inodekey(ino4) ∈ ri0, ri0[dentrykey(ino2, str)] ∈ fs0, ino ∈ dirs0, asynced → boolvar0, links(ino2, abs-dirs(fs0, ri0)) ≠ ∅ ∨ ino2 = ROOT_INO, m3 ≠ 0 ∨ fs0[ri0[dentrykey(ino3, str)]].ino = ROOT_INO, fs0[ri0[inodekey(ino0)]].nlink ≠ 0 ∨ ino0 = ROOT_INO, fs0[ri0[inodekey(ino1)]].nlink ≠ 0 ∨ ino1 = ROOT_INO, m0 ≠ 0 ∨ m = ROOT_INO, links(ino4, abs-dirs(fs0, ri0)) ≠ ∅ ∨ ino4 = ROOT_INO, links(m, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m = ROOT_INO, links(fs0[ri0[dentrykey(ino3, str)]].ino, abs-dirs(fs0, ri0)) ≠ ∅ ∨ fs0[ri0[dentrykey(ino3, str)]].ino = ROOT_INO, links(ino3, abs-dirs(fs0, ri0)) ≠ ∅ ∨ ino3 = ROOT_INO ⊦ ⟨afs_inode_sync#(mkinode(fs0[ri0[dentrykey(ino3, str)]].ino, md0, false, m3, 0, m6); dirs, files); p_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); c_inode := getinode(mkdentry(str, fs0[ri0[dentrykey(ino3, str)]].ino).ino, dirs, files); err := ESUCCESS; asynced := ?⟩ ( afs-cons(dirs, files) → dirs = abs-dirs (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino3, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino3, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino3, str)]].ino), adr3]) ∧ files = abs-files (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino3, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino3, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino3, str)]].ino), adr3]) ∧ orphans (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino3, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino3, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino3, str)]].ino), adr3]) = orphans(fs0, ri0) ∧ (asynced → boolvar) ∧ mkinode(m, md, true, m0, m1, m2 + 1) = p_inode ∧ mkinode(fs0[ri0[dentrykey(ino3, str)]].ino, md0, false, m3 + 1, 0, m6) = c_inode ∧ ESUCCESS = err), fs0[ri0[dentrykey(ino3, str)]].ino = 0, adr1 = adr3, adr1 = adr2, adr2 = adr3, m = 0, dentrykey(m, str0) ∈ ri0, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, ino ∈ files, m3 = 0 ∧ fs0[ri0[dentrykey(ino3, str)]].ino ≠ ROOT_INO, m0 = 0 ∧ m ≠ ROOT_INO, fs0[ri0[inodekey(ino1)]].nlink = 0 ∧ ino1 ≠ ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 129:
fs0[ri0[dentrykey(ino1, str)]].ino = fs0[ri0[dentrykey(ino3, str)]].ino, fs0[ri0[dentrykey(ino2, str)]] = dentrynode(key3, fs0[ri0[dentrykey(ino3, str)]].ino), fs0[ri0[inodekey(fs0[ri0[dentrykey(ino3, str)]].ino)]] = inodenode(key1, md2, false, m3, 0, m5), fs0[ri0[dentrykey(ino4, str)]] = dentrynode(key, fs0[ri0[dentrykey(ino3, str)]].ino), fs0[ri0[inodekey(m)]] = inodenode(key0, md1, true, m0, m1, m2), fs0[ri0[dentrykey(ino0, str)]] = dentrynode(key2, fs0[ri0[dentrykey(ino3, str)]].ino), dirs = abs-dirs(fs0, ri0)[m, mkdir(m2 + 1, md, m0, m1, abs-children(m, fs0, ri0)[str0, fs0[ri0[dentrykey(ino3, str)]].ino])], files = abs-files(fs0, ri0)[fs0[ri0[dentrykey(ino3, str)]].ino, mkfile(m5, md2, m3 + 1, abs-content(fs0[ri0[dentrykey(ino3, str)]].ino, fs0, ri0))], fs0[ri0[dentrykey(ino3, str)]].ino ≠ 0, adr1 ≠ adr3, adr1 ≠ adr2, adr2 ≠ adr3, m ≠ 0, fs0[ri0[inodekey(ino2)]].directory, fs0[ri0[inodekey(ino0)]].directory, fs0[ri0[inodekey(ino1)]].directory, fs0[ri0[inodekey(ino4)]].directory, fs0[ri0[inodekey(ino3)]].directory, fo.inodes?, orphans(fs0, ri0).inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino3, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino3, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino3, str)]].ino), adr3]), file-node-cons(fs0, ri0), log-cons (log0, fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino3, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino3, str)]].ino), md0, false, m3 + 1, 0, m6) ]), log-cons(log0, fs0), orphans-cons (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino3, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino3, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino3, str)]].ino), adr3], orphans(fs0, ri0)), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino3, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino3, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino3, str)]].ino), adr3], orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri-cons(ri0, fs0), ri-inj(ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino3, str)]].ino), adr3]), ri-inj(fi), ri-inj(ri0), ubifs-cons (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino3, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino3, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino3, str)]].ino), adr3], orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), inodekey(ino0) ∈ ri0, dentrykey(ino0, str) ∈ ri0, ri0[dentrykey(ino0, str)] ∈ fs0, dentrykey(ino2, str) ∈ ri0, inodekey(ino2) ∈ ri0, dentrykey(ino4, str) ∈ ri0, ri0[dentrykey(ino4, str)] ∈ fs0, inodekey(fs0[ri0[dentrykey(ino3, str)]].ino) ∈ ri0, ri0[inodekey(fs0[ri0[dentrykey(ino3, str)]].ino)] ∈ fs0, dentrykey(ino1, str) ∈ ri0, inodekey(ino1) ∈ ri0, ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, inodekey(ino3) ∈ ri0, dentrykey(ino3, str) ∈ ri0, inodekey(ino4) ∈ ri0, ri0[dentrykey(ino2, str)] ∈ fs0, ¬ dentrykey(m, str0) ∈ ri0, ¬ adr1 ∈ fs0, ¬ adr2 ∈ fs0, ¬ adr3 ∈ fs0, asynced → boolvar0, links(ino2, abs-dirs(fs0, ri0)) ≠ ∅ ∨ ino2 = ROOT_INO, m3 ≠ 0 ∨ fs0[ri0[dentrykey(ino3, str)]].ino = ROOT_INO, fs0[ri0[inodekey(ino0)]].nlink ≠ 0 ∨ ino0 = ROOT_INO, fs0[ri0[inodekey(ino1)]].nlink ≠ 0 ∨ ino1 = ROOT_INO, m0 ≠ 0 ∨ m = ROOT_INO, links(ino4, abs-dirs(fs0, ri0)) ≠ ∅ ∨ ino4 = ROOT_INO, links(m, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m = ROOT_INO, links(fs0[ri0[dentrykey(ino3, str)]].ino, abs-dirs(fs0, ri0)) ≠ ∅ ∨ fs0[ri0[dentrykey(ino3, str)]].ino = ROOT_INO, links(ino3, abs-dirs(fs0, ri0)) ≠ ∅ ∨ ino3 = ROOT_INO ⊦ ⟨afs_inode_sync#(mkinode(fs0[ri0[dentrykey(ino3, str)]].ino, md0, false, m3, 0, m6); dirs, files); p_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); c_inode := getinode(mkdentry(str, fs0[ri0[dentrykey(ino3, str)]].ino).ino, dirs, files); err := ESUCCESS; asynced := ?⟩ ( afs-cons(dirs, files) → dirs = abs-dirs (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino3, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino3, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino3, str)]].ino), adr3]) ∧ files = abs-files (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino3, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino3, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino3, str)]].ino), adr3]) ∧ orphans (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino3, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino3, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino3, str)]].ino), adr3]) = orphans(fs0, ri0) ∧ (asynced → boolvar) ∧ mkinode(m, md, true, m0, m1, m2 + 1) = p_inode ∧ mkinode(fs0[ri0[dentrykey(ino3, str)]].ino, md0, false, m3 + 1, 0, m6) = c_inode ∧ ESUCCESS = err), m3 = 0 ∧ fs0[ri0[dentrykey(ino3, str)]].ino ≠ ROOT_INO, m0 = 0 ∧ m ≠ ROOT_INO, fs0[ri0[inodekey(ino1)]].nlink = 0 ∧ ino1 ≠ ROOT_INO

Rule argument

Additional information

Used simplifier rules: ⊦ inodenode(key, md, boolvar, m, m0, m1).directory ↔ boolvar; (s)%⊦ ino ∈ abs-files(fs, ri) ↔ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory; (s)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (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][ino, ad0] = dirs[ino, ad0]; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)%⊦ ino ∈ abs-dirs(fs, ri) ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)