[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 11 from proof refine-rename-overwrite-keep-parent-different (previous step)

new_dent_inode.ino = fs[ri[dentrykey(new_inode.ino, str0)]].ino, old_dent_inode.ino = fs[ri[dentrykey(new_inode.ino, str)]].ino, new_inode.nlink = fs[ri[inodekey(new_inode.ino)]].nlink, new_inode.nsubdirs = fs[ri[inodekey(new_inode.ino)]].nsubdirs, new_inode.size = fs[ri[inodekey(new_inode.ino)]].size, ¬ fs[ri[inodekey(new_dent_inode.ino)]].directory ↔ ¬ fs[ri[inodekey(old_dent_inode.ino)]].directory, dirs = abs-dirs(fs, ri), err = err0, files = abs-files(fs, ri), new_child_inode = new_dent_inode, new_dent = mkdentry(str0, new_dent_inode.ino), old_dent = mkdentry(str, old_dent_inode.ino), old_parent_inode = mkinode(new_inode.ino, new_inode.meta, true, new_inode.nlink, new_inode.nsubdirs, new_inode.size), ro = orphans(fs, ri), new_dent_inode.ino ≠ ROOT_INO, new_dent_inode.nlink ≠ 0, new_inode.size ≠ 0, mkdentry(str, old_dent_inode.ino) ≠ mkdentry(str0, new_dent_inode.ino), new_inode.directory, fs[ri[inodekey(new_inode.ino)]].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_dent_inode.ino) ∈ ri, inodekey(new_dent_inode.ino) ∈ ri, dentrykey(new_inode.ino, str) ∈ ri, dentrykey(new_inode.ino, str0) ∈ ri, inodekey(new_inode.ino) ∈ ri, 1 ≤ new_inode.size, old_dent_inode.directory → 1 ≤ new_inode.nsubdirs, new_dent_inode.nlink = 1 → links(new_dent_inode.ino, fs, ri) = ∅ ++ dentrykey(new_inode.ino, str0), boolvar → boolvar0, fs[ri[inodekey(new_dent_inode.ino)]].directory → abs-children(new_dent_inode.ino, fs, ri) = ∅, fs[ri[inodekey(new_dent_inode.ino)]].directory → dentrykeys(inodekey(new_dent_inode.ino), ri) = ∅, new_inode.nlink ≠ 0 ∨ new_inode.ino = ROOT_INO, links(new_inode.ino, abs-dirs(fs, ri)) ≠ ∅ ∨ new_inode.ino = ROOT_INO, ¬ fs[ri[inodekey(old_dent_inode.ino)]].directory ∧ ¬ old_dent_inode.directory ∧ old_dent_inode.nlink = fs[ri[inodekey(old_dent_inode.ino)]].nlink ∧ old_dent_inode.nsubdirs = fs[ri[inodekey(old_dent_inode.ino)]].nsubdirs ∨ fs[ri[inodekey(old_dent_inode.ino)]].directory ∧ old_dent_inode.directory ∧ old_dent_inode.nlink = fs[ri[inodekey(old_dent_inode.ino)]].nlink ∧ old_dent_inode.nsubdirs = fs[ri[inodekey(old_dent_inode.ino)]].nsubdirs ∧ old_dent_inode.size = fs[ri[inodekey(old_dent_inode.ino)]].size, ¬ fs[ri[inodekey(old_dent_inode.ino)]].directory ∧ ¬ new_dent_inode.directory ∧ new_dent_inode.nlink = fs[ri[inodekey(new_dent_inode.ino)]].nlink ∧ new_dent_inode.nsubdirs = fs[ri[inodekey(new_dent_inode.ino)]].nsubdirs ∨ fs[ri[inodekey(new_dent_inode.ino)]].directory ∧ new_dent_inode.directory ∧ new_dent_inode.nlink = fs[ri[inodekey(new_dent_inode.ino)]].nlink ∧ new_dent_inode.nsubdirs = fs[ri[inodekey(new_dent_inode.ino)]].nsubdirs ∧ new_dent_inode.size = fs[ri[inodekey(new_dent_inode.ino)]].size, fs[ri[inodekey(old_dent_inode.ino)]].directory ∧ old_dent_inode.nlink = fs[ri[inodekey(old_dent_inode.ino)]].nlink ∧ old_dent_inode.size = fs[ri[inodekey(old_dent_inode.ino)]].size ∧ old_dent_inode.nsubdirs = fs[ri[inodekey(old_dent_inode.ino)]].nsubdirs ∧ old_dent_inode.directory ∨ ¬ fs[ri[inodekey(old_dent_inode.ino)]].directory ∧ old_dent_inode.nlink = fs[ri[inodekey(old_dent_inode.ino)]].nlink ∧ old_dent_inode.nsubdirs = 0 ∧ ¬ old_dent_inode.directory, fs[ri[inodekey(new_dent_inode.ino)]].directory ∧ new_dent_inode.nlink = fs[ri[inodekey(new_dent_inode.ino)]].nlink ∧ new_dent_inode.size = fs[ri[inodekey(new_dent_inode.ino)]].size ∧ new_dent_inode.nsubdirs = fs[ri[inodekey(new_dent_inode.ino)]].nsubdirs ∧ new_dent_inode.directory ∨ ¬ fs[ri[inodekey(old_dent_inode.ino)]].directory ∧ new_dent_inode.nlink = fs[ri[inodekey(new_dent_inode.ino)]].nlink ∧ new_dent_inode.nsubdirs = 0 ∧ ¬ new_dent_inode.directory ⊦ ⟪aubifs_rename_overwrite_keep_parent# (old_dent_inode.directory, old_dent_inode, fi, fo; old_parent_inode, new_child_inode, old_dent, new_dent, err, ri, ro, fs, log, boolvar0); new_parent_inode := old_parent_inode⟫ ⟨old_dent_inode0 := old_dent_inode; old_dent0 := mkdentry(str, old_dent_inode.ino); old_dent1 := mkdentry(str0, new_dent_inode.ino); old_inode := mkinode(new_inode.ino, new_inode.meta, true, new_inode.nlink, new_inode.nsubdirs, new_inode.size); 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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
new_dent_inode.ino = fs[ri[dentrykey(new_inode.ino, str0)]].ino, new_inode.nlink = fs[ri[inodekey(new_inode.ino)]].nlink, new_inode.nsubdirs = fs[ri[inodekey(new_inode.ino)]].nsubdirs, new_inode.size = fs[ri[inodekey(new_inode.ino)]].size, ¬ fs[ri[inodekey(new_dent_inode.ino)]].directory ↔ ¬ fs[ri[inodekey(m)]].directory, dirs = abs-dirs(fs, ri), err = err0, files = abs-files(fs, ri), m = fs[ri[dentrykey(new_inode.ino, str)]].ino, new_child_inode = new_dent_inode, new_dent = mkdentry(str0, new_dent_inode.ino), old_dent = mkdentry(str, m), old_dent_inode = mkinode(m, md, boolvar1, m0, m1, m2), old_parent_inode = mkinode(new_inode.ino, new_inode.meta, true, new_inode.nlink, new_inode.nsubdirs, new_inode.size), ro = orphans(fs, ri), fs[ri[inodekey(new_inode.ino)]].directory, new_inode.directory, 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-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), inodekey(new_inode.ino) ∈ ri, dentrykey(new_inode.ino, str0) ∈ ri, dentrykey(new_inode.ino, str) ∈ ri, inodekey(new_dent_inode.ino) ∈ ri, inodekey(m) ∈ ri, 1 ≤ new_inode.size, fs[ri[inodekey(new_dent_inode.ino)]].directory → dentrykeys(inodekey(new_dent_inode.ino), ri) = ∅, fs[ri[inodekey(new_dent_inode.ino)]].directory → abs-children(new_dent_inode.ino, fs, ri) = ∅, boolvar → boolvar0, new_dent_inode.nlink = 1 → links(new_dent_inode.ino, fs, ri) = ∅ ++ dentrykey(new_inode.ino, str0), boolvar1 → 1 ≤ new_inode.nsubdirs, fs[ri[inodekey(new_dent_inode.ino)]].directory ∧ new_dent_inode.nlink = fs[ri[inodekey(new_dent_inode.ino)]].nlink ∧ new_dent_inode.size = fs[ri[inodekey(new_dent_inode.ino)]].size ∧ new_dent_inode.nsubdirs = fs[ri[inodekey(new_dent_inode.ino)]].nsubdirs ∧ new_dent_inode.directory ∨ ¬ fs[ri[inodekey(m)]].directory ∧ new_dent_inode.nlink = fs[ri[inodekey(new_dent_inode.ino)]].nlink ∧ new_dent_inode.nsubdirs = 0 ∧ ¬ new_dent_inode.directory, fs[ri[inodekey(m)]].directory ∧ m0 = fs[ri[inodekey(m)]].nlink ∧ m2 = fs[ri[inodekey(m)]].size ∧ m1 = fs[ri[inodekey(m)]].nsubdirs ∧ boolvar1 ∨ ¬ fs[ri[inodekey(m)]].directory ∧ m0 = fs[ri[inodekey(m)]].nlink ∧ m1 = 0 ∧ ¬ boolvar1, ¬ fs[ri[inodekey(m)]].directory ∧ ¬ new_dent_inode.directory ∧ new_dent_inode.nlink = fs[ri[inodekey(new_dent_inode.ino)]].nlink ∧ new_dent_inode.nsubdirs = fs[ri[inodekey(new_dent_inode.ino)]].nsubdirs ∨ fs[ri[inodekey(new_dent_inode.ino)]].directory ∧ new_dent_inode.directory ∧ new_dent_inode.nlink = fs[ri[inodekey(new_dent_inode.ino)]].nlink ∧ new_dent_inode.nsubdirs = fs[ri[inodekey(new_dent_inode.ino)]].nsubdirs ∧ new_dent_inode.size = fs[ri[inodekey(new_dent_inode.ino)]].size, ¬ fs[ri[inodekey(m)]].directory ∧ ¬ boolvar1 ∧ m0 = fs[ri[inodekey(m)]].nlink ∧ m1 = fs[ri[inodekey(m)]].nsubdirs ∨ fs[ri[inodekey(m)]].directory ∧ boolvar1 ∧ m0 = fs[ri[inodekey(m)]].nlink ∧ m1 = fs[ri[inodekey(m)]].nsubdirs ∧ m2 = fs[ri[inodekey(m)]].size, links(new_inode.ino, abs-dirs(fs, ri)) ≠ ∅ ∨ new_inode.ino = ROOT_INO, new_inode.nlink ≠ 0 ∨ new_inode.ino = ROOT_INO ⊦ ⟪aubifs_rename_overwrite_keep_parent# (boolvar1, old_dent_inode, fi, fo; old_parent_inode, new_child_inode, old_dent, new_dent, err, ri, ro, fs, log, boolvar0); new_parent_inode := old_parent_inode⟫ ⟨old_dent_inode0 := old_dent_inode; old_dent0 := mkdentry(str, m); old_dent1 := mkdentry(str0, new_dent_inode.ino); old_inode := mkinode(new_inode.ino, new_inode.meta, true, new_inode.nlink, new_inode.nsubdirs, new_inode.size); 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_dent_inode.ino = ROOT_INO, new_dent_inode.nlink = 0, new_inode.size = 0, mkdentry(str, m) = mkdentry(str0, new_dent_inode.ino), new_inode.nlink = 0 ∧ new_inode.ino ≠ ROOT_INO

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [old_dent_inode, m, md, boolvar1, m0, m1, m2]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: old_dent_inode, m, md, boolvar1, m0, m1, m2