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Theorem add-in-09

⊦ sk ∈ fis → (addobj(r, class, fis, st)[r -- sk]) = fis[sk]

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: add-dupput, add-put-04, add-putbar-rew, addobj-addclass-sw, addobj-addobj-switch, addobj-delsw, addobj-union, addobj-union-rew, isobj-addobj-04,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 4
Proof steps: 10
Used lemmas: addobj-rec-01, addobj-base,
Used spec theorems:
- Used simplifier rules:
  - assoclist/fieldinit/assoc-no
  - assoclist/fieldinit/inkeys-nc
  - assoclist/fieldinit/assoc-yes
  - list/fieldinit-assoclista/a
  - pair/fieldinit/elim
  - list/fieldinit-assoclista/c
  - javastore/lookup-if
  - refkey/inj-01
  - assoclist/fieldinit/empty