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Theorem add-in-fskey

⊦ is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type → (r -- sk ∈ addarray(r, ty, vals, st) ↔ r -- sk ∈ st)

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: add-in-other, addarray-addaray, addarray-put-01, putarray-add-same, putarray-addarray-01, putarray-addarray-one,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 5
Proof steps: 10
Used lemmas: addarrayinit-base, addarrayinit-def, add-lastrec, in-1init-02, in-init-09,
Used spec theorems:
- Used simplifier rules:
  - storekey/test-02
  - storekey/test-01
  - list/javavalues/len
  - list/javavalues/len-02
  - nat-basic2/s
  - nat-basic1/ref-1
  - nat-basic2/a
  - nat-basic2/c
  - list/javavalues/a
  - list/javavalues/e-02
  - list-last/javavalues/last-elim
  - specialkeys/len
  - specialkeys/type-03
  - storekey/test-06
  - nat/pred-03
  - list-data/javavalues/size-01
  - javastore/instore-02
  - storefuns/instore-01