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Theorem pathex-put-pathex-array-refval

⊦ path∃(str, r, r1, st[r0 -- sk, val]) ∧ path∃(str, r, r0, st) ∧ ¬ path∃(str, val .refval, r1, st) ∧ is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < st[r0 -- _length] .intval ∧ is_referencevalue(val) ∧ validref(str, val .refval, st[r0 -- _type] .type .type, st) ∧ r0 ≠ jvmref ∧ is_arraytype(st[r0 -- _type] .type) ∧ (val .refval = jvmref → is_reftype(st[r0 -- _type] .type .type)) → path∃(str, r, r1, st)

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: 34
Proof steps: 86
Used lemmas: validrefs-null-02, pathex-array, pathex-trans, validrefs-postfix, pathex-def-simple, validrefs-one, pathex-not-is-validref-01, pathex-validrefs-in, validrefs-is-junk, validrefs-array, validrefs-put-notin, pathex-not-is-validref-02, pathex-one, pathex-def-nodups,
Used spec theorems:
- okfuns/is_array-put-okval
- list/references/In
- store/javastore/At-other
- list-last/references/l-02
Used simplifier rules:
- setlist/references/in
- set-union/references/int-ins
- setlist/references/list2set-rec
- setlist/references/list2set-empty
- set-union/references/int-e
- set-union/references/int-a
- set-union/references/int-c
- addfuns/is_valid_ref-isarray
- list/references/in-14
- list/references/in-15
- list/references/e-02
- list/references/first-02
- setlist/references/dups-03
- list-dup/references/a
- list/references/in-01
- list-dup/references/f-01
- list-last/references/lapp-01
- list-last/references/l-in
- int-abs/lels-04
- int-abs/lels-03
- javavalue/sel-09
- int-abs/lels
- int-abs/lels-01
- list-last/references/l-05
- list/references/c-08
- list/references/e
- list/references/app-02-ant
- refkey/inj-01
- list-dup/references/e-01
- list/references/in-empty
- list-last/references/lin-01
- int-abs/zero-gels-04
- javavalue/inj-03
- store/javastore/At-same
- oelem/intlista/lel
- storekey/inj-04
- refkey/inj
- list/references/in-06
- list-last/references/l-02
- list-last/references/l
- list/references/app
- javastore/length-at
- typefuns/array
- addfuns/is_valid_ref-01
- addfuns/is_obj-put-index
- addfuns/is_obj-type-02
- javatype/sel-01
- valuefuns/okval-refval
- typefuns/ref
- typefuns/subarray1
- addfuns/is_valid_ref-array
- list/references/in-17
- list/references/in-append
- list-dup/references/dups-cons
- list/references/a
- list/references/e-01
- list/references/c
- list-data/references/elim-list-c
- javastore/type-at
- javatype/test-09
- javatype/elim-01
- javavalue/test-19
- javavalue/elim-13
- storekey/test-08
- int-abs/forward-le-01
- int-abs/forward-le-05
- storekey/elim-04