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Theorem update-keyin-01

⊦ r -- sk ∈ update(r0, fis, st) ↔ r -- sk ∈ st ∨ r = r0 ∧ sk ∈ fis

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: onlymod-is-update, update-in, update-type-01,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 6
Proof steps: 10
Used lemmas: update-keyin, update-rec-01, update-empty,
Used spec theorems:
- store/javastore/In-insert
Used simplifier rules:
- refkey/inj
- assoclist/fieldinit/inone
- pair/fieldinit/sel-01
- pair/fieldinit/sel-02
- assoclist/fieldinit/in-append
- list/fieldinit-assoclista/a
- list/fieldinit-assoclista/c
- assoclist/fieldinit/empty