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Theorem addarrays-length

⊦ posints(ints) ∧ ints ≠ [] ∧ 0 ≤ i ∧ n→i(# (r ' + refs)) = countrefs(ints) ∧ is_newref_list(r ' + refs, st) → (addarrays(r ' + refs, ty, ints, i, st)[r -- _length]) = intval(ints .first)

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: addarrays-length-01,
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-length-first, addarrays-def, addarrays-empty,
Used spec theorems:
- Used simplifier rules:
  - nat-basic2/eq-01
  - intnat/add-nonneg-int-to-nat
  - int-abs/ler
  - int-abs/forward-le
  - int-basic1/forward-pos
  - oelem/intlista/transitivity
  - list/intlista/c-06
  - int-abs/lels
  - int-abs/anti
  - list/intlista/c-03
  - int-abs/numadd-01
  - intnat/nat2int-02
  - list-data/references/l
  - nat-basic2/one
  - oelem/intlista/lel
  - int-abs/forward-lsle
  - int-abs/forward-le-02
  - int-abs/forward-le-05
  - oelem/intlista/irreflexivity
  - int-basic1/lst-02
  - list/intlista/app
  - list-last/intlista/bin-01
  - list/references/app
  - list-last/intlista/b
  - list/intlista/in-empty
  - list/intlista/in-17
  - list/intlista/in-append
  - list/intlista/in-14
  - int-basic1/lst-01
  - int-abs/lels-04
  - int-abs/lels-01
  - list-data/references/size-01
  - int-basic2/ax-04
  - int-basic2/add-a
  - javavalue/inj-04
  - list/intlista/c-08
  - int-abs/zero-gels-04
  - int-basic2/add-c
  - list/intlista/app-02-ant
  - list/intlista/e
  - valuesfuns/posints-rec
  - list/intlista/a
  - list/intlista/e-01
  - list/intlista/c
  - int-abs/forward-le-01
  - nat-basic2/c
  - nat-basic2/a
  - intnat/n2i-add
  - list/references/a
  - list/references/len-02
  - list/references/len
  - list-data/intlista/elim-list-c