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Theorem hasSharing-dups-array

¬ hasSharing(r, st) ∧ is_arraytype(st[r -- _type] .type) ∧ r ≠ jvmref ⊦ ∀ i, j. i ≠ j ∧ 0 ≤ i ∧ i < st[r -- _length] .intval ∧ 0 ≤ j ∧ j < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ st[r -- i '] .refval ≠ jvmref → st[r -- i '] ≠ st[r -- j ']

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 4
Proof steps: 9
Used lemmas: fits-storekeys-one, hasSharing-def,
Used spec theorems:
- Used simplifier rules:
  - int-abs/lels-03
  - int-abs/lels
  - int-abs/lels-04
  - int-abs/lels-01
  - storekey/sel-06
  - storekey/test-08
  - javatype/diff-01
  - javavalue/sel-09
  - storefuns/lookup-one
  - list/storekeys/e
  - storekey/inj-04
  - list/storekeys/c-04
  - javavalue/test-19
  - int-abs/forward-le-01
  - int-abs/forward-le-05
  - javavalue/elim-13