[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 3 from proof rename-precond-abs (previous step)

old_dent.ino = fs[ri[dentrykey(old_parent_inode.ino, old_dent.name)]].ino, old_child_inode.ino = old_dent.ino, old_parent_inode.nlink = fs[ri[inodekey(old_parent_inode.ino)]].nlink, new_parent_inode.nlink = fs[ri[inodekey(new_parent_inode.ino)]].nlink, old_parent_inode.nsubdirs = fs[ri[inodekey(old_parent_inode.ino)]].nsubdirs, new_parent_inode.nsubdirs = fs[ri[inodekey(new_parent_inode.ino)]].nsubdirs, old_parent_inode.size = fs[ri[inodekey(old_parent_inode.ino)]].size, new_parent_inode.size = fs[ri[inodekey(new_parent_inode.ino)]].size, old_dent.dentry?, fs[ri[inodekey(old_parent_inode.ino)]].directory, old_parent_inode.directory, fs[ri[inodekey(new_parent_inode.ino)]].directory, new_parent_inode.directory, orphans(fs, ri).inodes?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), file-node-cons(fs, ri), log-cons(log, fs), 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), dentrykey(old_parent_inode.ino, old_dent.name) ∈ ri, inodekey(new_parent_inode.ino) ∈ ri, inodekey(old_parent_inode.ino) ∈ ri, new_parent_inode.ino = old_parent_inode.ino → new_parent_inode.meta = old_parent_inode.meta, (links(new_parent_inode.ino, abs-dirs(fs, ri)) ≠ ∅ ∨ new_parent_inode.ino = ROOT_INO) ∧ ¬ dentrykey(new_parent_inode.ino, new_dent.name) ∈ ri ∧ new_dent.negdentry? ∨ (links(new_parent_inode.ino, abs-dirs(fs, ri)) ≠ ∅ ∨ new_parent_inode.ino = ROOT_INO) ∧ (inodekey(new_dent.ino) ∈ ri ∧ fs[ri[inodekey(new_dent.ino)]].directory ∨ inodekey(new_dent.ino) ∈ ri ∧ ¬ fs[ri[inodekey(new_dent.ino)]].directory) ∧ dentrykey(new_parent_inode.ino, new_dent.name) ∈ ri ∧ new_dent.ino = fs[ri[dentrykey(new_parent_inode.ino, new_dent.name)]].ino ∧ new_dent.dentry? ∧ ( inodekey(new_child_inode.ino) ∈ ri ∧ fs[ri[inodekey(new_child_inode.ino)]].directory ∧ new_child_inode.nlink = fs[ri[inodekey(new_child_inode.ino)]].nlink ∧ new_child_inode.size = fs[ri[inodekey(new_child_inode.ino)]].size ∧ new_child_inode.nsubdirs = fs[ri[inodekey(new_child_inode.ino)]].nsubdirs ∧ new_child_inode.directory ∨ inodekey(new_child_inode.ino) ∈ ri ∧ ¬ fs[ri[inodekey(new_child_inode.ino)]].directory ∧ new_child_inode.nlink = fs[ri[inodekey(new_child_inode.ino)]].nlink ∧ new_child_inode.nsubdirs = 0 ∧ ¬ new_child_inode.directory) ∧ new_child_inode.ino = new_dent.ino ∧ ( inodekey(new_dent.ino) ∈ ri ∧ ¬ fs[ri[inodekey(new_dent.ino)]].directory ↔ inodekey(old_dent.ino) ∈ ri ∧ ¬ fs[ri[inodekey(old_dent.ino)]].directory) ∧ (inodekey(new_dent.ino) ∈ ri ∧ fs[ri[inodekey(new_dent.ino)]].directory → new_dent.ino ≠ ROOT_INO ∧ abs-children(new_dent.ino, fs, ri) = ∅), links(old_parent_inode.ino, abs-dirs(fs, ri)) ≠ ∅ ∨ old_parent_inode.ino = ROOT_INO, inodekey(old_dent.ino) ∈ ri ∧ fs[ri[inodekey(old_dent.ino)]].directory ∨ inodekey(old_dent.ino) ∈ ri ∧ ¬ fs[ri[inodekey(old_dent.ino)]].directory, inodekey(old_dent.ino) ∈ ri ∧ fs[ri[inodekey(old_dent.ino)]].directory ∧ old_child_inode.nlink = fs[ri[inodekey(old_dent.ino)]].nlink ∧ old_child_inode.size = fs[ri[inodekey(old_dent.ino)]].size ∧ old_child_inode.nsubdirs = fs[ri[inodekey(old_dent.ino)]].nsubdirs ∧ old_child_inode.directory ∨ inodekey(old_dent.ino) ∈ ri ∧ ¬ fs[ri[inodekey(old_dent.ino)]].directory ∧ old_child_inode.nlink = fs[ri[inodekey(old_dent.ino)]].nlink ∧ old_child_inode.nsubdirs = 0 ∧ ¬ old_child_inode.directory ⊦ ( new_dent.negdentry? ∧ (new_parent_inode.nlink ≠ 0 ∨ new_parent_inode.ino = ROOT_INO) ∧ ¬ dentrykey(new_parent_inode.ino, new_dent.name) ∈ ri ∨ new_dent.dentry? ∧ (new_parent_inode.nlink ≠ 0 ∨ new_parent_inode.ino = ROOT_INO) ∧ inodekey(new_dent.ino) ∈ ri ∧ dentrykey(new_parent_inode.ino, new_dent.name) ∈ ri ∧ fs[ri[dentrykey(new_parent_inode.ino, new_dent.name)]].ino = new_dent.ino ∧ ( inodekey(new_child_inode.ino) ∈ ri ∧ ¬ fs[ri[inodekey(new_child_inode.ino)]].directory ∧ ¬ new_child_inode.directory ∧ new_child_inode.nlink = fs[ri[inodekey(new_child_inode.ino)]].nlink ∧ new_child_inode.nsubdirs = fs[ri[inodekey(new_child_inode.ino)]].nsubdirs ∨ inodekey(new_child_inode.ino) ∈ ri ∧ fs[ri[inodekey(new_child_inode.ino)]].directory ∧ new_child_inode.directory ∧ new_child_inode.nlink = fs[ri[inodekey(new_child_inode.ino)]].nlink ∧ new_child_inode.nsubdirs = fs[ri[inodekey(new_child_inode.ino)]].nsubdirs ∧ new_child_inode.size = fs[ri[inodekey(new_child_inode.ino)]].size) ∧ new_child_inode.ino = new_dent.ino ∧ (¬ fs[ri[inodekey(new_dent.ino)]].directory ↔ ¬ fs[ri[inodekey(old_dent.ino)]].directory) ∧ (fs[ri[inodekey(new_dent.ino)]].directory → 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))) ∧ (old_parent_inode.nlink ≠ 0 ∨ old_parent_inode.ino = ROOT_INO) ∧ inodekey(old_dent.ino) ∈ ri ∧ ( ¬ fs[ri[inodekey(old_dent.ino)]].directory ∧ ¬ old_child_inode.directory ∧ old_child_inode.nlink = fs[ri[inodekey(old_dent.ino)]].nlink ∧ old_child_inode.nsubdirs = fs[ri[inodekey(old_dent.ino)]].nsubdirs ∨ fs[ri[inodekey(old_dent.ino)]].directory ∧ old_child_inode.directory ∧ old_child_inode.nlink = fs[ri[inodekey(old_dent.ino)]].nlink ∧ old_child_inode.nsubdirs = fs[ri[inodekey(old_dent.ino)]].nsubdirs ∧ old_child_inode.size = fs[ri[inodekey(old_dent.ino)]].size) ∧ 1 ≤ old_parent_inode.size ∧ (old_child_inode.directory → 1 ≤ old_parent_inode.nsubdirs)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

spec: dentry name: elim seq: ⊦ dent.dentry? → (str = dent.name ∧ m = dent.ino ↔ dent = mkdentry(str, m)) subst: [dent, str, m] → [old_dent, str, m]

Additional information

Used simplifier rules: ⊦ dent.dentry? → (str = dent.name ∧ m = dent.ino ↔ dent = mkdentry(str, m)); (elim) Used terms: old_dent, str, m