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Theorem init-at-01

⊦ j ≤ i ∧ i < j + n→i(# vals) → (addarray(r, vals, j, st)[r -- i ']) = vals[i→n(i - j)]

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: init-at, store-1init,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 2
Proof steps: 9
Used lemmas: addarrayinit-rec, addarrayinit-base,
Used spec theorems:
- Used simplifier rules:
  - int-abs/numadd-01
  - intnat/rax
  - list-del/javavalues/get-succ
  - int-abs/sub-add-05
  - int-abs/succ-01
  - int-basic1/ls-01
  - int-abs/lsone
  - int-basic2/ls-01
  - list-data/javavalues/l
  - nat-basic1/z
  - intnat/num-n2i-ls-02
  - int-abs/forward-le-05
  - int-abs/forward-lsle
  - int-abs/lels-02
  - list-del/javavalues/get-zero-01
  - int-abs/forward-le-01
  - int-abs/le-add
  - int-basic2/eq
  - int-abs/elim-sub
  - intnat/nat2int
  - int-abs/lep
  - int-abs/forward-lele
  - int-abs/lels
  - int-abs/lels-01
  - int-abs/succ-02
  - nat-basic2/c
  - nat-basic2/a
  - intnat/n2i-add
  - list/javavalues/len-02
  - list/javavalues/len
  - storekey/inj-04
  - refkey/inj-01
  - javastore/lookup-if
  - list/javavalues/a
  - list/javavalues/c
  - list-data/javavalues/size-01
  - int-basic2/ax-04
  - int-basic2/add-a
  - int-basic2/add-c
  - int-abs/lels-04