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Theorem px-parent

⊦ ispath(p, ino, m, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (px-parent(user, p, tree, abs-files(files)) ↔ px-parent(user, p, ino, dirs, files))

Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by: pr, pw,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 2
Proof steps: 5
Used lemmas: px, ispath-target, path-in-eq, path-in,
Used spec theorems:
- Used simplifier rules:
  - afs-base/isexpath
  - afs-base/path-in-dirs
  - directory-tree/nil-at
  - path-permission/posix-permission/px-parent-eps
  - path-permission/vfs-permission/px-parent-eps
  - path-permission/vfs-permission/px-parent-noneps
  - path-permission/posix-permission/px-parent-noneps
  - list/path/e-02
  - list/path/a
  - directory-tree/split-in
  - path/parent-elim