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Theorem abs-is-file

⊦ ¬ ino ∈ dirs → (((abs(tree, ino) * D))(dirs) ↔ tree = fnode(⌜ino⌝ ) ∧ D(dirs))

Type: A user defined theorem
Validity: The proof is valid.
Features: ws, lws,
Comment:
Used by: abs-meta-h, abs-nlinks-h, abs-path-h, path-fid,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 1
Proof steps: 5
Used lemmas: abs-dnode, abs-fnode,
Used spec theorems:
- Used simplifier rules:
  - heap-sep/dir-heap/trueH
  - heap-sep/dir-heap/true-rev
  - file-id-data/sel
  - maplet/dir-heap/ex3-shift
  - maplet/dir-heap/map-in
  - directory-tree-base/fnode-inj
  - heap-sep/dir-heap/prop
  - heap-sep/dir-heap/and
  - heap-sep/dir-heap/and-com
  - heap-sep/dir-heap/and-ass
  - heap-sep/dir-heap/sep-com
  - heap-sep/dir-heap/sep-ass
  - heap-sep/dir-heap/emp-sep
  - heap-sep/dir-heap/prop-shift
  - file-id-data/elim