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Theorem getarray-in-01

⊦ 0 < i1 → (val ∈ getarray(r, i0, i1, st) ↔ (∃ i. i0 ≤ i ∧ i < i0 + i1 ∧ st[r -- i '] = val))

Type: A user defined theorem
Validity: The proof is valid.
Features:
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: 25
Used lemmas: getArray-one, getArray-rec,
Used spec theorems:
- Used simplifier rules:
  - oelem/intlista/lel
  - int-abs/forward-le-01
  - int-abs/lep
  - int-abs/forward-lele
  - int-abs/succ-02
  - int-abs/anti
  - int-basic2/ls
  - int-basic2/ls-01
  - int-abs/lels-04
  - int-basic1/ls-01
  - int-basic2/add-less
  - int-abs/forward-lels
  - int-abs/lels-03
  - intnat/abs-succ-03
  - nat-basic2/s
  - intnat/labs
  - int-abs/abs-16
  - nat-basic2/a
  - nat-basic2/c
  - int-basic2/ax-04
  - int-abs/numsub
  - int-basic2/zero-02
  - int-abs/numls-02
  - int-abs/elim-sub
  - int-basic1/forward-pos
  - list/javavalues/a
  - list/javavalues/in-append
  - list/javavalues/Last
  - oelem/intlista/irreflexivity
  - int-basic2/add-c
  - int-basic2/add-a
  - int-abs/succ-01
  - list/javavalues/in-17
  - int-abs/bet
  - int-abs/forward-le-05
  - int-abs/lels
  - int-abs/lels-01