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Theorem abs-delorphans

∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs, ∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files, abs(tree, ROOT_INO)(dirs) ⊦ dirs \ orphans(dirs, files) = dirs

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 7
Proof steps: 17
Used lemmas: abs-path-h, abs-has-rootpath,
Used spec theorems:
- heap/dir-heap/ext
- afs-base/orphans
- list/path/lastdiv-rew
- afs-base/path-split
Used simplifier rules:
- set-basic/open-file-handles/size-zero-01
- set-basic/open-file-handles/ne-01
- heap/dir-heap/at-diffs
- heap/dir-heap/in-diffs
- heap-sep/dir-heap/emp-sep
- heap-sep/dir-heap/sep-ass
- heap-sep/dir-heap/sep-com
- afs-base/isexpath
- directory-tree/nil-in
- afs-base/path-here
- afs-base/valid-ino
- afs-base/path-in-dirs
- list/path/a
- directory-tree/split-in
- afs-base/path-one
- afs-base/links-nonempty
- abstract-dir/elim