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Theorem in-keys-elim

⊦ key ∈ keys(fs, ax) ↔ (∃ adr. adr ∈ ax ∧ fs[adr].key = key)

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: 0
Proof steps: 9
Used lemmas:
Used spec theorems:
- Used simplifier rules:
  - aubifs-base/keys-base
  - list/key-list-set/in-empty
  - list/address-list-set/in-empty
  - list/address-list-set/in-rec
  - list/key-list-set/a
  - list/key-list-set/in-rec
  - list/address-list-set/a
  - list/key-list-set/c
  - aubifs-base/keys-rec
  - list/address-list-set/c