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Theorem synced-dirs-add-update-clean-inode

⊦ ino ∈ icache ∧ ¬ icache[ino].dirty → (synced(dirs, icache[ino, mkientry(false, inode)], pcache) ↔ synced(dirs, icache, pcache))

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 8
Proof steps: 27
Used lemmas: synced-ino, synced-dirs,
Used spec theorems:
- Used simplifier rules:
  - icache-entry/elim
  - pcache-entry/elim
  - store/icache/insin
  - store/icache/At-same
  - pcache-entry/sel-02
  - icache-entry/inj
  - icache-entry/sel-02
  - store/icache/in-neq
  - store/icache/At-other