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Theorem hassharing-validrefs-dups

⊦ dups(refs) ∧ validrefs(str, refs, st[refs .first -- _type] .type, st) → hasSharing(refs .first, st)

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 38
Proof steps: 83
Used lemmas: fits-storekeys-rec, fits-append, hasSharing-def, ex-validrefs-fits-stronger,
Used spec theorems:
- cyclic/validrefs-nopathex
- list/references/In
- list-del/references/get-last
- storefuns/lookup-append
- list/references/a
- list/references/Noassoc
- cyclic/validrefs-prefix
- cyclic/validrefs-is-junk
- cyclic/validrefs-class
- cyclic/validrefs-array
- storefuns/lookup-rec-01
- cyclic/validrefs-postfix
Used simplifier rules:
- cyclic/validrefs-sametype
- list-dup/references/c-02
- addfuns/is_obj-arraytype
- storekey/test-07
- fieldspec/elim
- addfuns/is_valid_ref-isobj
- okfuns/is_array-classtype
- int-abs/lels-03
- int-abs/lels
- int-abs/lels-04
- int-abs/lels-01
- storekey/sel-06
- storekey/test-08
- addfuns/instfields-index
- list/storekeys/e
- list/storekeys/app-01
- list/storekeys/c
- javavalue/elim-13
- int-abs/forward-le-01
- int-abs/forward-le-05
- addfuns/isarray-isobj-01
- addfuns/is_valid_ref
- typefuns/ref
- list/references/in-06
- list/references/fr
- nat-basic2/s
- list/references/app
- list/references/in-empty
- javavalue/sel-09
- javavalue/test-19
- valuefuns/refval-xtra
- javavalue/elim-refval
- cyclic/validrefs-null-02
- list/storekeys/app-02-ant
- list/storekeys/a
- list/storekeys/app-04
- nat-basic2/oz
- list-data/storekeys/size-01
- list-del/storekeys/first-all
- nat-basic1/ref-1
- list-data/storekeys/l
- nat/lels-01
- nat-basic1/z
- list/references/c-08
- nat-basic2/c
- nat-basic2/a
- nat/add-num-01
- list/references/len-02
- list/references/len
- list/references/app-02-ant
- list/references/e
- cyclic/validrefs-not
- cyclic/pathex-one
- list-dup/references/rec
- list/references/a
- list/references/e-01
- list/references/c
- cyclic/validrefs-empty
- list-dup/references/e-01
- list-data/references/elim-list-c