[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 20 from proof refine-mkdir (previous step)

err = err0, ino = ROOT_INO, path0 ≠ ε, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), of-cons(of, dirs, files), psynced → asynced ⊦ [vfs_walk#(parent(path0), user, dirs, files, asynced; ino, err); dent := negdentry(path0.last); if err = ESUCCESS then vfs_may_create#(ino, dent, user, dirs, files, asynced; inode, err); if err = ESUCCESS then afs_check_commit#(dirs, files; err; asynced); fs := abs-files(files); if err = ESUCCESS then afs_mkdir#(md; inode, c_inode, dent, err, dirs, files; asynced)] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_mkdir#(path0, md, user, fs, abs-of(of); err0, root; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err0))

User applied rule insert program lemma

And obtained the following new goals

Rule argument

spec: vfs-asm name: walk-prepost-parent seq: ino = ROOT_INO, afs-cons(dirs, files), p ≠ ε ⊦ ⟪vfs_walk#(parent(p), user, dirs, files, asynced; ino, err)⟫ ∃ q, str. p = q + str ∧ ( ⌊err⌋ ∨ err = ESUCCESS ∧ ispath(q, ROOT_INO, ino, dirs, files) ∧ px-parent(user, q, ROOT_INO, dirs, files) ∨ err = ENOENT ∧ ¬ ispath(q, ROOT_INO, dirs, files) ∨ err = EACCESS ∧ (∃ p'. p' ⊑ q ∧ ispath(p', ROOT_INO, dirs, files) ∧ ¬ px(user, p', ROOT_INO, dirs, files))) subst: [asynced, files, dirs, user, p, err, ino] → [asynced, files, dirs, user, path0, err, ino] flags: <all paths>

Additional information