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Theorem succ-1init

⊦ 0 < i ∧ i ≤ n→i(# vals) → (addarray(r, ty, val + vals, st)[r -- i ']) = (addarray(r, ty, vals, st)[r -- (i - 1) '])

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 1
Proof steps: 4
Used lemmas: add-at-ok,
Used spec theorems:
- Used simplifier rules:
  - list-del/javavalues/get-succ
  - intnat/rax-04
  - int-abs/numle-02
  - int-abs/numleledel-01
  - list/javavalues/len
  - list/javavalues/len-02
  - list/javavalues/a
  - intnat/n2i-add
  - nat-basic2/a
  - nat-basic2/c
  - int-basic2/ls-01
  - int-abs/lels
  - int-abs/lels-03
  - int-abs/forward-le-01
  - int-abs/succ-01
  - int-basic2/add-c
  - int-basic2/add-a
  - int-abs/mone-06
  - int-abs/numls-02
  - list-data/javavalues/l
  - nat-basic1/z
  - intnat/num-n2i-ls-02
  - int-abs/forward-le-05
  - int-abs/forward-le
  - list/javavalues/c
  - int-abs/elim-sub