[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 295 from proof refine-link (previous step)

fs[ri[dentrykey(ino1, str)]].ino = fs[ri[dentrykey(ino2, str)]].ino, fs[ri[dentrykey(ino3, str)]].ino = fs[ri[dentrykey(ino2, str)]].ino, 0 = fs[ri[inodekey(fs[ri[dentrykey(ino2, str)]].ino)]].nsubdirs, fs[ri[dentrykey(ino0, str)]] = dentrynode(key, fs[ri[dentrykey(ino2, str)]].ino), dirs = abs-dirs(fs, ri) [m0, mkdir (fs[ri[inodekey(m0)]].size + 1, fs[ri[inodekey(m0)]].meta, fs[ri[inodekey(m0)]].nlink, fs[ri[inodekey(m0)]].nsubdirs, abs-children(m0, fs, ri)[str0, fs[ri[dentrykey(ino2, str)]].ino]) ], files = files0[ino, files0[ino].nlink:= (files0[ino].nlink + 1)], files0 = abs-files(fs, ri), ino = mkdentry(str, fs[ri[dentrykey(ino2, str)]].ino).ino, fs[ri[dentrykey(ino2, str)]].dentry?, mkdentry(str, fs[ri[dentrykey(ino2, str)]].ino).dentry?, fs[ri[inodekey(ino0)]].directory, fs[ri[inodekey(m0)]].directory, fs[ri[inodekey(ino1)]].directory, fs[ri[inodekey(ino3)]].directory, fs[ri[inodekey(ino2)]].directory, 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), dentrykey(ino0, str) ∈ ri, ri[dentrykey(ino0, str)] ∈ fs, inodekey(ino0) ∈ ri, inodekey(m0) ∈ ri, dentrykey(ino1, str) ∈ ri, inodekey(fs[ri[dentrykey(ino2, str)]].ino) ∈ ri, inodekey(ino1) ∈ ri, dentrykey(ino3, str) ∈ ri, dentrykey(ino2, str) ∈ ri, inodekey(ino2) ∈ ri, inodekey(ino3) ∈ ri, ri[dentrykey(ino2, str)] ∈ fs, asynced → boolvar0, ∀ adr, adr0, adr1. adr ∈ fs ∨ adr0 ∈ fs ∨ adr1 ∈ fs ∨ adr = adr0 ∨ adr = adr1 ∨ adr0 = adr1, links(fs[ri[dentrykey(ino2, str)]].ino, abs-dirs(fs, ri)) ≠ ∅ ∨ fs[ri[dentrykey(ino2, str)]].ino = ROOT_INO, links(m0, abs-dirs(fs, ri)) ≠ ∅ ∨ m0 = ROOT_INO, links(ino0, abs-dirs(fs, ri)) ≠ ∅ ∨ ino0 = ROOT_INO, fs[ri[inodekey(m0)]].nlink ≠ 0 ∨ m0 = ROOT_INO, fs[ri[inodekey(ino1)]].nlink ≠ 0 ∨ ino1 = ROOT_INO, fs[ri[inodekey(ino3)]].nlink ≠ 0 ∨ ino3 = ROOT_INO, fs[ri[inodekey(fs[ri[dentrykey(ino2, str)]].ino)]].nlink ≠ 0 ∨ fs[ri[dentrykey(ino2, str)]].ino = ROOT_INO, links(ino2, abs-dirs(fs, ri)) ≠ ∅ ∨ ino2 = ROOT_INO ⊦ ⟨afs_inode_sync#(mkinode(m0, md, true, fs[ri[inodekey(m0)]].nlink, fs[ri[inodekey(m0)]].nsubdirs, fs[ri[inodekey(m0)]].size); dirs, files); afs_inode_sync# (mkinode(fs[ri[dentrykey(ino2, str)]].ino, md0, false, fs[ri[inodekey(fs[ri[dentrykey(ino2, str)]].ino)]].nlink, 0, m6); dirs, files); p_inode := (m0 ∈ dirs ⊃ mkinode(m0, dirs[m0].meta, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size) ;mkinode(m0, files[m0].meta, false, files[m0].nlink, 0, files[m0].size) ); c_inode := getinode(mkdentry(str, fs[ri[dentrykey(ino2, str)]].ino).ino, dirs, files); err := ESUCCESS; asynced := ?⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ (asynced → boolvar) ∧ mkinode(m0, md, true, fs[ri[inodekey(m0)]].nlink, fs[ri[inodekey(m0)]].nsubdirs, fs[ri[inodekey(m0)]].size) = p_inode ∧ mkinode(fs[ri[dentrykey(ino2, str)]].ino, md0, false, fs[ri[inodekey(fs[ri[dentrykey(ino2, str)]].ino)]].nlink, 0, m6) = c_inode ∧ negdentry(str0) = mkdentry(str0, mkdentry(str, fs[ri[dentrykey(ino2, str)]].ino).ino) ∧ ENOSPC = err), ∃ err0. ⌊err0⌋ ∧ ⟨err := err0; asynced := ?⟩ ((asynced → boolvar) ∧ ENOSPC = err), fs[ri[dentrykey(ino2, str)]].ino = 0, m0 = 0, fs[ri[inodekey(fs[ri[dentrykey(ino2, str)]].ino)]].directory, dentrykey(m0, str0) ∈ ri, fs[ri[inodekey(ino1)]].nlink = 0 ∧ ino1 ≠ ROOT_INO, fs[ri[inodekey(m0)]].nlink = 0 ∧ m0 ≠ ROOT_INO, fs[ri[inodekey(fs[ri[dentrykey(ino2, str)]].ino)]].nlink = 0 ∧ fs[ri[dentrykey(ino2, str)]].ino ≠ ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ mkdentry(str, m) ≠ negdentry(str0); (s)% ⊦ mkdentry(str, m).dentry?; (s)% ⊦ mkfile(m, md, m0, content).nlink:= m2 = mkfile(m, md, m2, content); (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)%⊦ abs-file(ino, fs, ri) = mkfile (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, abs-content(ino, fs, ri)); (s)%⊦ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory → abs-files(fs, ri)[ino] = abs-file(ino, fs, ri); (s)% ⊦ mkdentry(str, m).ino = m; (s)