[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 332 from proof refine-link (previous step)

fs[ri[dentrykey(ino2, str)]].ino = fs[ri[dentrykey(ino0, str)]].ino, fs[ri[dentrykey(ino1, str)]].ino = fs[ri[dentrykey(ino0, str)]].ino, 0 = fs[ri[inodekey(fs[ri[dentrykey(ino0, str)]].ino)]].nsubdirs, dirs = abs-dirs(fs, ri), files = abs-files(fs, ri), old_dent0 = negdentry(str0), p_inode0 = mkinode(m, md, true, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, fs[ri[inodekey(m)]].size), p_inode1 = mkinode(fs[ri[dentrykey(ino0, str)]].ino, md0, false, fs[ri[inodekey(fs[ri[dentrykey(ino0, str)]].ino)]].nlink, 0, m6), fs[ri[dentrykey(ino0, str)]].ino ≠ 0, m ≠ 0, fs[ri[dentrykey(ino0, str)]].dentry?, fs[ri[inodekey(ino2)]].directory, fs[ri[inodekey(ino1)]].directory, fs[ri[inodekey(m)]].directory, fs[ri[inodekey(ino0)]].directory, fs[ri[inodekey(fs[ri[dentrykey(ino0, str)]].ino)]].inode?, fs[ri[inodekey(m)]].inode?, fo.inodes?, orphans(fs, ri).inodes?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, orphans(fs, ri)), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), ri-cons(ri, fs), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), dentrykey(ino0, str) ∈ ri, ri[dentrykey(ino0, str)] ∈ fs, dentrykey(ino2, str) ∈ ri, inodekey(ino1) ∈ ri, dentrykey(ino1, str) ∈ ri, inodekey(ino0) ∈ ri, ri[inodekey(fs[ri[dentrykey(ino0, str)]].ino)] ∈ fs, inodekey(fs[ri[dentrykey(ino0, str)]].ino) ∈ ri, ri[inodekey(m)] ∈ fs, inodekey(m) ∈ ri, inodekey(ino2) ∈ ri, ⌊err0⌋ , ¬ fs[ri[inodekey(fs[ri[dentrykey(ino0, str)]].ino)]].directory, ¬ dentrykey(m, str0) ∈ ri, asynced → boolvar0, fs[ri[inodekey(fs[ri[dentrykey(ino0, str)]].ino)]].nlink ≠ 0 ∨ fs[ri[dentrykey(ino0, str)]].ino = ROOT_INO, fs[ri[inodekey(ino2)]].nlink ≠ 0 ∨ ino2 = ROOT_INO, fs[ri[inodekey(ino1)]].nlink ≠ 0 ∨ ino1 = ROOT_INO, fs[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO, links(ino0, abs-dirs(fs, ri)) ≠ ∅ ∨ ino0 = ROOT_INO, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO, links(fs[ri[dentrykey(ino0, str)]].ino, abs-dirs(fs, ri)) ≠ ∅ ∨ fs[ri[dentrykey(ino0, str)]].ino = ROOT_INO ⊦ ⟨afs_link#(mkdentry(str, fs[ri[dentrykey(ino0, str)]].ino); p_inode0, p_inode1, old_dent0, err1, dirs, files; asynced)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ (asynced → boolvar) ∧ mkinode(m, md, true, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, fs[ri[inodekey(m)]].size) = p_inode0 ∧ mkinode(fs[ri[dentrykey(ino0, str)]].ino, md0, false, fs[ri[inodekey(fs[ri[dentrykey(ino0, str)]].ino)]].nlink, 0, m6) = p_inode1 ∧ negdentry(str0) = old_dent0 ∧ err0 = err1), fs[ri[inodekey(fs[ri[dentrykey(ino0, str)]].ino)]].nlink = 0 ∧ fs[ri[dentrykey(ino0, str)]].ino ≠ ROOT_INO, fs[ri[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO, fs[ri[inodekey(ino1)]].nlink = 0 ∧ ino1 ≠ ROOT_INO

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 333:
fs[ri[dentrykey(ino1, str)]].ino = m0, fs[ri[dentrykey(ino2, str)]].ino = m0, 0 = fs[ri[inodekey(m0)]].nsubdirs, fs[ri[dentrykey(ino0, str)]] = dentrynode(key, m0), dirs = abs-dirs(fs, ri), files = abs-files(fs, ri), old_dent0 = negdentry(str0), p_inode0 = mkinode(m, md, true, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, fs[ri[inodekey(m)]].size), p_inode1 = mkinode(m0, md0, false, fs[ri[inodekey(m0)]].nlink, 0, m6), fs[ri[dentrykey(ino0, str)]].dentry?, fs[ri[inodekey(ino0)]].directory, fs[ri[inodekey(m)]].directory, fs[ri[inodekey(ino1)]].directory, fs[ri[inodekey(ino2)]].directory, fs[ri[inodekey(m)]].inode?, fs[ri[inodekey(m0)]].inode?, orphans(fs, ri).inodes?, fo.inodes?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, orphans(fs, ri)), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), ri-cons(ri, fs), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), inodekey(ino2) ∈ ri, inodekey(m) ∈ ri, ri[inodekey(m)] ∈ fs, inodekey(m0) ∈ ri, ri[inodekey(m0)] ∈ fs, inodekey(ino0) ∈ ri, dentrykey(ino1, str) ∈ ri, inodekey(ino1) ∈ ri, dentrykey(ino2, str) ∈ ri, ri[dentrykey(ino0, str)] ∈ fs, dentrykey(ino0, str) ∈ ri, ⌊err0⌋ , asynced → boolvar0, links(m0, abs-dirs(fs, ri)) ≠ ∅ ∨ m0 = ROOT_INO, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO, links(ino0, abs-dirs(fs, ri)) ≠ ∅ ∨ ino0 = ROOT_INO, fs[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO, fs[ri[inodekey(ino1)]].nlink ≠ 0 ∨ ino1 = ROOT_INO, fs[ri[inodekey(ino2)]].nlink ≠ 0 ∨ ino2 = ROOT_INO, fs[ri[inodekey(m0)]].nlink ≠ 0 ∨ m0 = ROOT_INO ⊦ ⟨afs_link#(mkdentry(str, m0); p_inode0, p_inode1, old_dent0, err1, dirs, files; asynced)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ (asynced → boolvar) ∧ mkinode(m, md, true, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, fs[ri[inodekey(m)]].size) = p_inode0 ∧ mkinode(m0, md0, false, fs[ri[inodekey(m0)]].nlink, 0, m6) = p_inode1 ∧ negdentry(str0) = old_dent0 ∧ err0 = err1), m = 0, m0 = 0, fs[ri[inodekey(m0)]].directory, dentrykey(m, str0) ∈ ri, fs[ri[inodekey(ino1)]].nlink = 0 ∧ ino1 ≠ ROOT_INO, fs[ri[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO, fs[ri[inodekey(m0)]].nlink = 0 ∧ m0 ≠ ROOT_INO

Rule argument

spec: node name: elim-02 seq: ⊦ nd.dentry? → (key = nd.key ∧ m = nd.ino ↔ nd = dentrynode(key, m)) subst: [nd, key, m] → [fs[ri[dentrykey(ino0, str)]], key, m0]

Additional information

Used simplifier rules: ⊦ nd.dentry? → (key = nd.key ∧ m = nd.ino ↔ nd = dentrynode(key, m)); (elim) Used terms: fs[ri[dentrykey(ino0, str)]], key, m0