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Theorem validrefs-put-array-badindex

⊦ i < 0 → (validrefs(str, refs, ty, st[r -- i ', val]) ↔ validrefs(str, refs, ty, st))

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: pathex-put-array-badindex,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 19
Proof steps: 60
Used lemmas: validrefs-array, validrefs-class, validrefs-null-01, validrefs-null-02, validrefs-is-junk, validrefs-empty,
Used spec theorems:
- addfuns/is-valid-ref-stronger-def
- store/javastore/At-other
- addfuns/isvalidref-put-array-badindex
Used simplifier rules:
- addfuns/isvalidref-put-array-badindex
- int-abs/forward-lels
- refkey/inj-01
- refkey/inj
- storekey/inj-04
- oelem/intlista/lel
- store/javastore/At-same
- int-abs/lels-04
- oelem/intlista/transitivity
- int-abs/zero-gels-01
- int-abs/forward-le-01
- int-abs/forward-le-05
- int-abs/forward-lsle
- int-abs/lels-01
- addfuns/is_valid_ref-isarray
- javastore/length-at
- addfuns/is_valid_ref-01
- addfuns/isarray-isobj-01
- int-abs/lels-03
- javavalue/sel-09
- fieldspec/sel-03
- javavalue/test-19
- javavalue/elim-13
- fieldspec/elim
- list/references/e-01
- list-data/references/elim-list-c
- javastore/at-other
- addfuns/is_obj-put-index
- addfuns/is_valid_ref-put-index
- javastore/type-at
- list/references/app
- list/references/a
- int-abs/lels
- list/references/c
- int-abs/forward-le-02