[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 4 from proof refine-rename-overwrite-reparent-dir (previous step)

dirs = abs-dirs(fs, ri), err = err0, files = abs-files(fs, ri), new_child_inode = new_dent_inode, new_dent = old_dent1, new_parent_inode = new_inode, old_child_inode = old_dent_inode, old_dent = old_dent0, old_parent_inode = old_inode, orphans(dirs, files) = abs-keys(ro), new_dent_inode.directory, ro.inodes?, fo.inodes?, afs-cons(dirs, files), file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, ro), pre-rename(old_inode, old_dent, old_dent_inode, new_inode, new_dent, new_dent_inode, dirs, files), replay-cons-strong(fs, ri, ro, fi, fo, log), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, ro, fi, fo, log), valid-dentry(new_parent_inode.ino, new_dent, dirs, files), boolvar → boolvar0, dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ orphans(dirs, files) = abs-keys(ro) ∧ afs-cons(dirs, files) ∧ ro.inodes? ∧ file-node-cons(fs, ri) ∧ log-cons(log, fs) ∧ replay-cons-strong(fs, ri, ro, fi, fo, log) ∧ ri-inj(ri) ∧ ri-inj(fi) ∧ ubifs-cons(fs, ri, ro, fi, fo, log) ∧ pre-rename(old_inode, old_dent, old_dent_inode, new_inode, new_dent, new_dent_inode, dirs, files) → pre-rename(old_inode, old_dent, old_dent_inode, new_inode, new_dent, new_dent_inode, fs, ri, ro) ⊦ ⟪aubifs_rename_overwrite_reparent# (old_child_inode.directory, old_child_inode, fi, fo ; old_parent_inode, new_parent_inode, new_child_inode, old_dent, new_dent, err, ri, ro, fs, log, boolvar0)⟫ ⟨afs_rename#(; old_inode, new_inode, old_dent_inode, new_dent_inode, old_dent0, old_dent1, err0, dirs, files; boolvar)⟩ ( (dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ orphans(dirs, files) = abs-keys(ro) ∧ (boolvar → boolvar0)) ∧ old_parent_inode = old_inode ∧ new_parent_inode = new_inode ∧ old_child_inode = old_dent_inode ∧ new_child_inode = new_dent_inode ∧ old_dent = old_dent0 ∧ new_dent = old_dent1 ∧ err = err0), old_parent_inode.ino = new_parent_inode.ino

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
new_dent_inode.ino = old_dent1.ino, old_dent1.ino = fs[ri[dentrykey(new_inode.ino, old_dent1.name)]].ino, old_dent_inode.ino = old_dent0.ino, old_dent0.ino = fs[ri[dentrykey(old_inode.ino, old_dent0.name)]].ino, new_dent_inode.nlink = fs[ri[inodekey(old_dent1.ino)]].nlink, new_inode.nlink = fs[ri[inodekey(new_inode.ino)]].nlink, old_inode.nlink = fs[ri[inodekey(old_inode.ino)]].nlink, old_dent_inode.nlink = fs[ri[inodekey(old_dent0.ino)]].nlink, new_dent_inode.nsubdirs = fs[ri[inodekey(old_dent1.ino)]].nsubdirs, new_inode.nsubdirs = fs[ri[inodekey(new_inode.ino)]].nsubdirs, old_inode.nsubdirs = fs[ri[inodekey(old_inode.ino)]].nsubdirs, old_dent_inode.nsubdirs = fs[ri[inodekey(old_dent0.ino)]].nsubdirs, new_dent_inode.size = fs[ri[inodekey(old_dent1.ino)]].size, new_inode.size = fs[ri[inodekey(new_inode.ino)]].size, old_inode.size = fs[ri[inodekey(old_inode.ino)]].size, old_dent_inode.size = fs[ri[inodekey(old_dent0.ino)]].size, abs-children(old_dent1.ino, fs, ri) = ∅, dentrykeys(inodekey(old_dent1.ino), ri) = ∅, dirs = abs-dirs(fs, ri), err = err0, files = abs-files(fs, ri), new_child_inode = new_dent_inode, new_dent = old_dent1, new_parent_inode = new_inode, old_dent = old_dent0, old_parent_inode = old_inode, ro = orphans(fs, ri), old_dent1.ino ≠ ROOT_INO, old_inode.ino ≠ new_inode.ino, new_dent_inode.nlink ≠ 0, old_inode.nsubdirs ≠ 0, old_inode.size ≠ 0, old_dent0.dentry?, old_dent1.dentry?, new_inode.directory, old_inode.directory, fs[ri[inodekey(old_inode.ino)]].directory, fs[ri[inodekey(old_dent1.ino)]].directory, fs[ri[inodekey(new_inode.ino)]].directory, new_dent_inode.directory, fs[ri[inodekey(old_dent0.ino)]].directory, old_dent_inode.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-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), inodekey(old_dent0.ino) ∈ ri, dentrykey(old_inode.ino, old_dent0.name) ∈ ri, inodekey(old_inode.ino) ∈ ri, inodekey(old_dent1.ino) ∈ ri, dentrykey(new_inode.ino, old_dent1.name) ∈ ri, inodekey(new_inode.ino) ∈ ri, 1 ≤ old_inode.size, 1 ≤ old_inode.nsubdirs, new_dent_inode.nlink = 1 → links(old_dent1.ino, fs, ri) = ∅ ++ dentrykey(new_inode.ino, old_dent1.name), boolvar → boolvar0, old_inode.nlink ≠ 0 ∨ old_inode.ino = ROOT_INO, new_inode.nlink ≠ 0 ∨ new_inode.ino = ROOT_INO, links(old_inode.ino, abs-dirs(fs, ri)) ≠ ∅ ∨ old_inode.ino = ROOT_INO, links(new_inode.ino, abs-dirs(fs, ri)) ≠ ∅ ∨ new_inode.ino = ROOT_INO ⊦ ⟪aubifs_rename_overwrite_reparent# (true, old_dent_inode, fi, fo; old_parent_inode, new_parent_inode, new_child_inode, old_dent, new_dent, err, ri, ro, fs, log, boolvar0)⟫ ⟨old_dent_inode0 := old_dent_inode; afs_rename#(; old_inode, new_inode, old_dent_inode, new_dent_inode, old_dent0, old_dent1, err0, dirs, files; boolvar)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(ro) ∧ (boolvar → boolvar0) ∧ old_parent_inode = old_inode ∧ new_parent_inode = new_inode ∧ old_dent_inode0 = old_dent_inode ∧ new_child_inode = new_dent_inode ∧ old_dent = old_dent0 ∧ new_dent = old_dent1 ∧ err = err0), new_inode.nlink = 0 ∧ new_inode.ino ≠ ROOT_INO, old_inode.nlink = 0 ∧ old_inode.ino ≠ ROOT_INO

Rule argument

Additional information

Used simplifier rules: ⊦ inodekey(m).ino = m; (s)% ⊦ inodekey(m).inode?; (s)%⊦ key ∈ orphans(fs, ri) ↔ key.inode? ∧ key ∈ ri ∧ fs[ri[key]].nlink = 0 ∧ key.ino ≠ ROOT_INO; (s)%ubifs-parent-in: ⊦ dentrykey(ino, str) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → inodekey(ino) ∈ ri; (forward) from specification aubifs-inv%not-zero: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward) from specification nat% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ {key} = ∅ ++ key; (s)%⊦ valid-dir-inode(inode, fs, ri) ↔ valid-dir-ino(inode.ino, fs, ri) ∧ (inode.directory ↔ fs[ri[inodekey(inode.ino)]].directory) ∧ inode.nlink = fs[ri[inodekey(inode.ino)]].nlink ∧ inode.nsubdirs = fs[ri[inodekey(inode.ino)]].nsubdirs ∧ inode.size = fs[ri[inodekey(inode.ino)]].size; (s)%⊦ valid-file-ino(ino, fs, ri) ↔ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory; (s)%⊦ valid-file-inode(inode, fs, ri) ↔ valid-file-ino(inode.ino, fs, ri) ∧ (inode.directory ↔ fs[ri[inodekey(inode.ino)]].directory) ∧ inode.nlink = fs[ri[inodekey(inode.ino)]].nlink ∧ inode.nsubdirs = fs[ri[inodekey(inode.ino)]].nsubdirs; (s)%⊦ valid-wb-inode(inode, fs, ri) ↔ valid-file-inode(inode, fs, ri) ∨ valid-dir-inode(inode, fs, ri); (s)% ⊦ valid-ino(ino, fs, ri) ↔ inodekey(ino) ∈ ri; (s)%⊦ valid-dir-ino(ino, fs, ri) ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory; (s)%⊦ valid-parent-ino(ino, fs, ri, ro) ↔ ( valid-dir-ino(ino, fs, ri) ∧ (fs[ri[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO)) ∧ ¬ inodekey(ino) ∈ ro; (s)%⊦ valid-dentry(ino, dent, fs, ri, ro) ↔ dent.dentry? ∧ valid-parent-ino(ino, fs, ri, ro) ∧ valid-ino(dent.ino, fs, ri) ∧ dentrykey(ino, dent.name) ∈ ri ∧ fs[ri[dentrykey(ino, dent.name)]].ino = dent.ino; (s)%⊦ valid-negdentry(ino, dent, fs, ri, ro) ↔ dent.negdentry? ∧ valid-parent-ino(ino, fs, ri, ro) ∧ ¬ dentrykey(ino, dent.name) ∈ ri; (s)%⊦ pre-rename (old_parent_inode, old_dent, old_child_inode, new_parent_inode, new_dent, new_child_inode, fs, ri, ro) ↔ ( valid-negdentry(new_parent_inode.ino, new_dent, fs, ri, ro) ∨ valid-dentry(new_parent_inode.ino, new_dent, fs, ri, ro) ∧ valid-wb-inode(new_child_inode, fs, ri) ∧ new_child_inode.ino = new_dent.ino ∧ ( valid-file-ino(new_dent.ino, fs, ri) ↔ valid-file-ino(old_dent.ino, fs, ri)) ∧ ( valid-dir-ino(new_dent.ino, fs, ri) → new_dent.ino ≠ ROOT_INO ∧ dentrykeys(inodekey(new_dent.ino), ri) = ∅) ∧ new_child_inode.ino ≠ ROOT_INO ∧ new_child_inode.nlink ≠ 0 ∧ ( new_child_inode.nlink = 1 → links(new_child_inode.ino, fs, ri) = {dentrykey(new_parent_inode.ino, new_dent.name)} )) ∧ valid-dentry(old_parent_inode.ino, old_dent, fs, ri, ro) ∧ valid-dir-inode(new_parent_inode, fs, ri) ∧ valid-dir-inode(old_parent_inode, fs, ri) ∧ ( new_parent_inode.ino = old_parent_inode.ino → new_parent_inode.meta = old_parent_inode.meta) ∧ valid-wb-inode(old_child_inode, fs, ri) ∧ old_child_inode.ino = old_dent.ino ∧ old_parent_inode.size ≥ 1 ∧ (old_child_inode.directory → old_parent_inode.nsubdirs ≥ 1); (s)%⊦ dentrykey(ino, str) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[inodekey(ino)]].directory; (ss)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) → ri-inj(ri); (ss)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) → log-cons(log, fs); (ss)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) → ro.inodes?; (ss)% ⊦ 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)% ⊦ dir-empty(ino, dirs, files) ↔ dirs[ino].entries = ∅; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)%⊦ valid-file-inode(inode, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory; (s)% ⊦ mkdir(m, md, m0, m1, entries).nsubdirs = m1; (s)% ⊦ mkdir(m, md, m0, m1, entries).size = m; (s)% ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (s)% ⊦ valid-dir-ino(ino, dirs, files) ↔ ino ∈ dirs; (s)%⊦ valid-dir-inode(inode, dirs, files) ↔ valid-dir-ino(inode.ino, dirs, files) ∧ inode.nlink = dirs[inode.ino].nlink ∧ inode.size = dirs[inode.ino].size ∧ inode.nsubdirs = dirs[inode.ino].nsubdirs ∧ inode.directory; (s)%⊦ valid-wb-inode(inode, dirs, files) ↔ valid-dir-inode(inode, dirs, files) ∨ valid-file-inode(inode, dirs, files); (s)%⊦ valid-negdentry(ino, dent, dirs, files) ↔ valid-parent-ino(ino, dirs, files) ∧ ¬ dent.name ∈ dirs[ino].entries ∧ dent.negdentry?; (s)%⊦ pre-rename (old_parent_inode, old_dent, old_child_inode, new_parent_inode, new_dent, new_child_inode, dirs, files) ↔ ( valid-negdentry(new_parent_inode.ino, new_dent, dirs, files) ∨ valid-dentry(new_parent_inode.ino, new_dent, dirs, files) ∧ valid-wb-inode(new_child_inode, dirs, files) ∧ new_child_inode.ino = new_dent.ino ∧ ( valid-file-ino(new_dent.ino, dirs, files) ↔ valid-file-ino(old_dent.ino, dirs, files)) ∧ ( valid-dir-ino(new_dent.ino, dirs, files) → new_dent.ino ≠ ROOT_INO ∧ dir-empty(new_dent.ino, dirs, files))) ∧ valid-dentry(old_parent_inode.ino, old_dent, dirs, files) ∧ valid-dir-inode(old_parent_inode, dirs, files) ∧ valid-dir-inode(new_parent_inode, dirs, files) ∧ ( new_parent_inode.ino = old_parent_inode.ino → new_parent_inode.meta = old_parent_inode.meta) ∧ valid-wb-inode(old_child_inode, dirs, files) ∧ old_child_inode.ino = old_dent.ino; (s)%⊦ dentrykey(ino, str) ∈ ri → abs-children(ino, fs, ri)[str] = fs[ri[dentrykey(ino, str)]].ino; (s)% ⊦ str ∈ abs-children(ino, fs, ri) ↔ dentrykey(ino, str) ∈ ri; (s)% ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)%⊦ abs-dir(ino, fs, ri) = mkdir (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, fs[ri[inodekey(ino)]].nsubdirs, abs-children(ino, fs, ri)); (s)%⊦ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory → abs-dirs(fs, ri)[ino] = abs-dir(ino, fs, ri); (s)%⊦ ino ∈ abs-files(fs, ri) ↔ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory; (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)%⊦ ino ∈ abs-dirs(fs, ri) ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory; (s)%⊦ valid-parent-ino(ino, dirs, files) ↔ ino ∈ dirs ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO); (s)%⊦ valid-dentry(ino, dent, dirs, files) ↔ valid-parent-ino(ino, dirs, files) ∧ valid-ino(dent.ino, dirs, files) ∧ dent.name ∈ dirs[ino].entries ∧ dent.ino = dirs[ino].entries[dent.name] ∧ dent.dentry?; (s)%⊦ ro.inodes? → (abs-keys(ro) = abs-keys(orphans(fs, ri)) ↔ ro = orphans(fs, ri)); (s)%⊦ afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)) → orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(orphans(fs, ri)); (s)