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Theorem validrefs-put-notin-03

⊦ val .refval ≠ refs0 .first ∧ refs0 .first ≠ st[r -- sk] .refval ∧ refs0 ≠ [] ∧ sk ≠ _type ∧ sk ≠ _length ∧ ¬ dups(refs + r ' + refs0) ∧ (is_valid_ref(str, r, st) ↔ is_valid_ref(str, r, st[r -- sk, val])) → (validrefs(str, refs + r ' + refs0, ty, st[r -- sk, val]) ↔ validrefs(str, refs + r ' + refs0, ty, st))

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: 45
Proof steps: 116
Used lemmas: validrefs-not, validrefs-array, validrefs-put-notin, validrefs-class, validrefs-null-02, validrefs-is-junk,
Used spec theorems:
- okfuns/is_array-arraytype
- addfuns/is_obj-arraytype
- store/javastore/At-other
- addfuns/is_valid_ref-def
Used simplifier rules:
- okfuns/is_array-put-01
- list/references/e-03
- list/references/in-17
- list/references/in-append
- list/references/in-14
- list/references/in-15
- list/references/e-02
- list/references/first-02
- javastore/look-ins
- addfuns/is_obj-put-01
- addfuns/is_valid_ref-put-01
- int-abs/forward-lels
- specialkeys/len
- specialkeys/type-03
- int-abs/lels-03
- int-abs/lels-04
- int-abs/forward-le-01
- int-abs/forward-le-05
- addfuns/is_valid_ref-isarray
- okfuns/is_array-arraytype
- addfuns/is_obj-isarray
- addfuns/is_valid_ref-01
- int-abs/lels
- int-abs/lels-01
- list/references/in-01
- refkey/inj-01
- refkey/inj
- store/javastore/At-same
- javavalue/sel-09
- fieldspec/sel-03
- javavalue/test-19
- javavalue/elim-13
- fieldspec/elim
- addfuns/is_valid_ref-isobj
- addfuns/is_obj-arraytype
- addfuns/isarray-isobj-01
- addfuns/is_valid_ref
- list/references/c-08
- javastore/at-other-16
- list/references/e
- list/references/app-02-ant
- addfuns/is_valid_ref-null
- list/references/in-empty
- list-dup/references/e-01
- list/references/Nil
- set-union/references/int-e
- setlist/references/list2set-empty
- list-dup/references/dups-cons
- list/references/in-06
- list/references/e-01
- set-union/references/int-c
- set-union/references/int-a
- setlist/references/in
- set-union/references/int-ins
- setlist/references/list2set-rec
- list/references/c
- setlist/references/dups-03
- list-dup/references/a
- list/references/a
- list-dup/references/f-01
- list-data/references/elim-list-c