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Theorem ri-closed-gc-one

⊦ key ∈ ri ∧ ¬ adr ∈ fs ∧ ri-closed(ri, fs, ro) ∧ ri-cons(ri, fs) → ri-closed(ri[key, adr], fs[adr, fs[ri[key]]], ro)

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: 49
Used lemmas: node-closed, ri-closed, ri-cons,
Used spec theorems:
- Used simplifier rules:
  - node-store/in-insert
  - store/node-store/k-At-same
  - store/node-store/notmemlookup
  - node/elim-02
  - node/test-03
  - node/test-02
  - node/elim-05
  - node/test-13
  - node/test-22
  - store/node-store/At-other
  - store/node-index/k-At-same
  - store/node-store/At-same
  - store/node-store/At-in-out
  - store/node-index/insin
  - key/inj-03
  - store/node-index/At-other
  - store/node-index/in-neq
  - store/node-index/In-insert
  - store/node-index/At-same