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Theorem entries-recdel

⊦ str ∈ sdt → abs(sdt, sdi) = (⌜str ∈ sdi⌝ ∧ abs(sdt -- str, sdi -- str) * abs(sdt[str], sdi[str]))

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: abs-dir-h, abs-nlinks-h, abs-path-h, abs-paths-eq, abs-tree, entries-unfold, path-unfold,
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: abs-rec,
Used spec theorems:
- store/directory-tree-inst/exin
Used simplifier rules:
- store/directory-tree-inst/Del-rec-same
- store/directory-tree-inst/notin-del-notin
- directory-tree-base/At-same
- heap-sep/dir-heap/And-prop-inj
- heap-sep/dir-heap/sep-com
- heap-sep/dir-heap/and-ass
- heap-sep/dir-heap/and-com