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Theorem walk-prepost-parent

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)))

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: inv-create, inv-link, inv-mkdir, inv-renam, inv-rmdir, inv-unlink,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 4
Proof steps: 19
Used lemmas: walk-prepost,
Used spec theorems:
- Used simplifier rules:
  - list/path/Last
  - list-last/path/b-01
  - list-data/path/elim-list-c
  - list/path/app-04
  - list/path/c
  - error/disj-29
  - error/disj-07
  - error-class/eaccess
  - afs-base/expath-rec
  - afs-base/valid-dir-ino
  - afs-base/path-rec
  - list-last/path/bc
  - list/path/app-08
  - list-last/path/butlast-last
  - abstract-dir/elim
  - afs-base/afs-cons-root-dir
  - afs-base/afs-cons-dir-nlink
  - list/path/app-02
  - list/path/e
  - list-last/path/last-elim
  - list/path/in-rec
  - list/path/in-17
  - list/path/in-append
  - list/path/in-15
  - list/path/in-14
  - list/path/e-01
  - path-permission/vfs-permission/px-prefix
  - list/path/a
  - list-last/path/prefix-app