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Theorem keys-in

⊦ key ∈ ns.keys ↔ (∃ n. key = inodekey(n) ∧ n ∈ ns)

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 2
Proof steps: 4
Used lemmas: keys-inodekeys, keys-inodekey-in,
Used spec theorems:
- Used simplifier rules:
  - set-basic/node-index/size-zero-01
  - set-basic/node-index/ne-01
  - aubifs-inv/inodes-nodentry
  - aubifs-inv/inodes-nodata
  - key/inj-03