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Theorem px

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

Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by: px-parent, px-prefix, py, refine-link,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 5
Proof steps: 12
Used lemmas: fid-file, path-in-eq, path-in,
Used spec theorems:
- path-permission/posix-permission/px
- path-permission/vfs-permission/px
- vfs-abs/abs-meta-h
Used simplifier rules:
- afs-base/isexpath
- afs-base/afs-cons-notfile
- heap-sep/dir-heap/emp-sep
- heap-sep/dir-heap/sep-ass
- heap-sep/dir-heap/sep-com
- afs-base/path-prefix
- posix-base/meta-dir
- afs-base/path-in-dirs