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Theorem in-1dim-15

⊦ 0 ≤ j ∧ j < i → r -- j ' ∈ addarray(r, val, i, st)

Type: A user defined theorem
Validity: The proof is valid.
Features: localsimp,
Comment:
Used by: in-1dim-16, in-1dim-other-index, in-1dim-other-index-01,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 3
Proof steps: 8
Used lemmas: addarray-rec,
Used spec theorems:
- Used simplifier rules:
  - oelem/intlista/lel
  - int-abs/anti
  - int-abs/lels-04
  - int-abs/lels-01
  - int-basic1/ls-01
  - intnat/abs-succ-03
  - nat-basic2/s
  - intnat/labs
  - int-abs/abs-16
  - oelem/intlista/irreflexivity
  - nat-basic2/a
  - nat-basic2/c
  - int-abs/mone-06
  - int-abs/numls-02
  - int-abs/lels-02
  - int-abs/succ-02
  - int-basic2/add-c
  - int-basic2/add-a
  - int-basic2/add-in
  - int-abs/elim-sub
  - int-abs/sub-eq
  - storekey/inj-04
  - refkey/inj-01
  - store/javastore/In-insert
  - int-abs/ax-02
  - int-abs/lels
  - int-abs/lels-03
  - int-abs/forward-le-01
  - int-abs/forward-le-05