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Theorem absc-path

⊦ p ∈ tree ∧ ((abs|(tree, ino, p, ino0) * D))(dirs) ∧ ispath(p, ino, ino1, dirs, files) → ino0 = ino1

Type: A user defined theorem
Validity: The proof is valid.
Features: forward, localforward,
Comment:
Used by: abs-meta-h, abs-nlinks-h, abs-paths-eq, abs-unshared-h,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 2
Proof steps: 8
Used lemmas: entries-dom2, absc-entries, absc-dnode-rec, absc-emp,
Used spec theorems:
- Used simplifier rules:
  - directory-tree/nil-in
  - afs-base/path-here
  - afs-base/valid-ino
  - heap-sep/dir-heap/emp-sep
  - heap-sep/dir-heap/false-rev
  - heap-sep/dir-heap/falseH
  - afs-base/valid-dir-ino
  - afs-base/path-rec
  - directory-tree/split-in
  - list/path/c
  - abstract-dir/elim
  - directory-tree/one-inf
  - abstract-dir/sel-09
  - abstract-dir/sel-03
  - directory-tree/one-at
  - store/dir-entries/Del-in
  - afs-base/path-in-dirs
  - maplet/dir-heap/map-in
  - maplet/dir-heap/at-eq
  - heap-sep/dir-heap/prop
  - heap-sep/dir-heap/and
  - maplet/dir-heap/ex3-shift
  - heap-sep/dir-heap/and-com
  - heap-sep/dir-heap/and-ass
  - heap-sep/dir-heap/prop-shift
  - list/path/a
  - store/directory-tree-inst/notin-del-notin
  - directory-tree-inst/read-notin
  - directory-tree/one-ind
  - heap-sep/dir-heap/sep-ass
  - heap-sep/dir-heap/sep-com