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Theorem in-dels-ro

⊦ key ∈ ri ⊖ ks ↔ key ∈ ri ∧ ¬ key ∈ ks ∧ (key.data? → ¬ inodekey(key.ino) ∈ ks)

Type: A user defined theorem
Validity: The proof is valid.
Features: ws, lws,
Comment:
Used by: del-commute-dels, del-del-again, del-merge-dels, del-put-again, dels-ignore-data, in-dels-inode, notin-dels,
Used by units in proved state: aubifs-inv,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 1
Proof steps: 2
Used lemmas: datakeys-set, dels-with-data,
Used spec theorems:
- Used simplifier rules:
  - store+set/node-index/Diff-ext