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Theorem hasSharing-put-index-refval

⊦ disjoint(str, r ' + r2 ', st) ∧ ¬ hasSharing(r, st) ∧ ¬ hasSharing(r2, st) ∧ ¬ junkref(str, r, st) ∧ r ≠ r2 ∧ validref(str, r2, st[r0 -- _type] .type .type, st) ∧ r0 ≠ jvmref ∧ is_arraytype(st[r0 -- _type] .type) ∧ (r2 = jvmref → is_reftype(st[r0 -- _type] .type .type)) → ¬ hasSharing(r, st[r0 -- i ', refval(r2)])

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: 219
Proof steps: 625
Used lemmas: fits-storekeys-rec, hasSharing-def-better, hasSharing-self, disjoint-def-fits, fits-storekeys-empty, fits-rec, fits-null, fits-append, fits-put-other, hasSharing-def,
Used spec theorems:
Used simplifier rules:
- junkrefs/validref-null
- javastore/look-ins
- list/storekeys/app-01
- int-abs/forward-lels
- list/references/in-17
- list/references/in-06
- list/javavalues/a
- junkrefs/validreflist-rec-01
- junkrefs/validreflist-one-01
- junkrefs/validref-object
- junkrefs/validref-object-01
- list/references/a
- valuesfuns/mkvalsr-one
- valuesfuns/mkvalsr-rec
- javatype/test-16
- list/storekeys/app-04
- int-abs/zero-gels-04
- storefuns/lookup-one
- list/storekeys/app
- int-abs/forward-le-01
- int-abs/forward-le-05
- javatype/diff-01
- junkrefs/junkref-bad-type
- store/javastore/At-same
- list/storekeys/e-02
- list-last/storekeys/prefix-empty
- javavalue/inj-03
- storefuns/lookup-empty
- list/storekeys/Nil
- javavalue/elim-13
- javastore/length-at
- storekey/sel-06
- storekey/test-08
- addfuns/instfields-index
- javastore/type-at
- list/storekeys/c-07
- list/storekeys/c-08
- list/storekeys/e-01
- list-last/storekeys/postifx-app-03
- list-last/storekeys/prefix-one
- javavalue/sel-09
- list/storekeys/app-02-ant
- list/storekeys/e
- list/storekeys/a
- list/storekeys/e-03
- specialkeys/len
- specialkeys/type-03
- list/storekeys/Last
- list/storekeys/c
- javavalue/test-19
- valuefuns/refval-xtra
- javavalue/elim-refval
- javatype/test-09
- javatype/elim-01