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Theorem path-in-eq

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

Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by: abs-acyclic, abs-unfold, dir-empty, dir-entry, fid-ino, fid-ino-entry, path-in, path-in-last, pr, pw, px, px-parent, px-prefix, py, py-prefix, py-strong, refine-create, refine-fsync, refine-link, refine-mkdir, refine-open, refine-readdir, refine-readmeta, refine-rmdir, refine-truncate, refine-unlink, refine-writemeta,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 1
Proof steps: 3
Used lemmas: fid-file,
Used spec theorems:
- vfs-abs/abs-path-h
Used simplifier rules:
- afs-base/afs-cons-notfile
- heap-sep/dir-heap/emp-sep
- heap-sep/dir-heap/sep-ass
- heap-sep/dir-heap/sep-com