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Theorem addarrays-refin

⊦ ¬ r ∈ refs → (r -- sk ∈ addarrays(refs, ty, ints, i, st) ↔ r -- sk ∈ st)

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 4
Proof steps: 12
Used lemmas: countrefs-getdims-01, getdims-zeroin-01, countdims-rec, countdims-zero, countrefs-zero, getdims-zero, getdims-rec, getdims-posints-01, getdims-empty-01, multi-in-other, addarrays-def, addarrays-empty,
Used spec theorems:
- Used simplifier rules:
  - intnat/n2n
  - int-abs/ler
  - int-abs/zero-gels-04
  - int-abs/forward-le
  - oelem/intlista/irreflexivity
  - int-abs/forward-le-05
  - list/intlista/c-06
  - int-abs/lels
  - int-abs/anti
  - list/intlista/c-03
  - intnat/num-n2i-eq
  - oelem/intlista/lel
  - int-abs/forward-le-02
  - list/intlista/app
  - list-last/intlista/bin-01
  - list-last/intlista/b
  - list/intlista/in-empty
  - list/intlista/in-17
  - list/intlista/in-append
  - list/intlista/in-14
  - int-abs/lels-04
  - int-abs/lels-01
  - list/intlista/e
  - list/intlista/app-02-ant
  - int-abs/forward-le-01
  - valuesfuns/posints-rec
  - list/intlista/a
  - list/intlista/e-01
  - list/intlista/c
  - list-data/intlista/elim-list-c