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Theorem getarray-offset

j0 ≤ j, 0 ≤ j0 ⊦ getarray(r, i, j, st) = getarray(r, i, j0, st) + getarray(r, i + j0, j - j0, st)

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: bar-neq, getarray-offset-01, getarray-offset-02, getbar-anyrec,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 8
Proof steps: 14
Used lemmas: get-empty, get-zero, getArray-one, getArray-zero, getArray-rec,
Used spec theorems:
- Used simplifier rules:
  - int-basic2/ls
  - int-abs/sub-add-09
  - int-abs/lels-04
  - int-abs/succ-01
  - int-abs/sub-le-01
  - intnat/rax-01
  - nat/pred-03
  - int-abs/zero-gels
  - int-abs/lels-01
  - int-abs/minus-sub
  - int-abs/minus-add
  - int-abs/leone
  - intnat/num-i2n-le-02
  - int-basic1/ls-01
  - nat/ls-01
  - nat-basic2/s
  - intnat/labs
  - int-abs/abs
  - oelem/intlista/irreflexivity
  - nat-basic2/a
  - nat-basic2/c
  - list/javavalues/app-03
  - int-abs/Sub-def
  - int-abs/sub-sub
  - int-abs/ler
  - int-abs/sub-le
  - int-abs/les
  - int-basic2/neq-01
  - int-abs/numsub
  - int-abs/sub-add
  - list/javavalues/app-01
  - int-abs/lep
  - int-abs/zero-gels-04
  - int-abs/mone-06
  - int-abs/numls-02
  - int-abs/numleledel-01
  - int-abs/numle-02
  - int-abs/forward-lsle
  - int-abs/forward-le
  - int-abs/sub-ls-01
  - int-basic1/forward-pos
  - list/javavalues/Last
  - int-abs/sub-eq-01
  - list/javavalues/app
  - list/javavalues/c-04
  - int-abs/numleledel
  - int-abs/forward-le-05
  - int-abs/bet
  - int-abs/lels-02
  - int-abs/anti
  - int-abs/neg-06
  - list/javavalues/Nil
  - list/javavalues/a
  - int-abs/negle-13
  - int-basic2/ax-04
  - int-basic2/add-a
  - int-basic2/add-c
  - int-abs/forward-le-01
  - int-abs/forward-lele
  - int-abs/lels