[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 580 from proof refine-rmdir (previous step)

root[q + str '] = dnode(md1, ∅), dirs[ino1] = mkdir(# entries0, md2, # links(ino1, dirs), m1, entries0), dirs[entries0[str]] = mkdir(0, md, # links(entries0[str], dirs), m2, ∅), files0 = files, root[q].dir?, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pw(user, md2), px(user, md2), px-parent(user, q, ROOT_INO, dirs, files), entries0[str] ∈ dirs, ino1 ∈ dirs, str ∈ entries0, ⌊err0⌋ , psynced → asynced0, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [vfs_put_inode#(mkinode(entries0[str], md, true, # links(entries0[str], dirs), m2, 0), of, asynced; err0, dirs, files)] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_rmdir#(q + str ', user, abs-files(files0), abs-of(of); err1, root; psynced)⟩ (abs-files(files0) = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err0 = err1))

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 581:
dirs[entries0[str]] = mkdir(0, md, # links(entries0[str], dirs), m2, ∅), dirs[ino1] = mkdir(# entries0, md2, # links(ino1, dirs), m1, entries0), root[q + str '] = dnode(md1, ∅), err = err0, files0 = files, p_inode = mkinode(entries0[str], md, true, # links(entries0[str], dirs), m2, 0), root.dir?, root[q].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pw(user, md2), px(user, md2), px-parent(user, q, ROOT_INO, dirs, files), str ∈ entries0, ino1 ∈ dirs, entries0[str] ∈ dirs, ⌊err0⌋ , psynced → asynced0, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [if err = ESUCCESS ∧ ¬ is-open(p_inode.ino, of) then afs_evict#(p_inode, asynced; err, dirs, files)] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_rmdir#(q + str ', user, abs-files(files0), abs-of(of); err1, root; psynced)⟩ (abs-files(files0) = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err1))

Rule argument

pos: right 1

Additional information

Used simplifier rules: vfs_put_inode#(DEL_INODE, OF, ASYNCED; ERR, DIRS, FILES) {if ERR = ESUCCESS ∧ ¬ is-open(DEL_INODE.ino, OF) then afs_evict#(DEL_INODE, ASYNCED; ERR, DIRS, FILES) };