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Theorem walk-prepost

ino = ROOT_INO, afs-cons(dirs, files) ⊦ ⟪vfs_walk#(p, user, dirs, files, asynced; ino, err)⟫ ( ⌊err⌋ ∨ err = ESUCCESS ∧ ispath(p, ROOT_INO, ino, dirs, files) ∧ px-parent(user, p, ROOT_INO, dirs, files) ∨ err = ENOENT ∧ ¬ ispath(p, ROOT_INO, dirs, files) ∨ err = EACCESS ∧ p ≠ ε ∧ (∃ p'. p' ⊑ parent(p) ∧ 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-fsync, inv-link, inv-open, inv-readdir, inv-readmeta, inv-truncate, inv-writemeta, walk-prepost-parent,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 2
Proof steps: 3
Used lemmas: walk-prepost-h, walk-term,
Used spec theorems:
- Used simplifier rules:
  - afs-base/path-here
  - afs-base/valid-ino
  - list/path/Nil
  - list/path/a
  - afs-base/afs-cons-root-dir