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Theorem hasSharing-pathex

⊦ ¬ hasSharing(r, st) ∧ path∃(str, r, r0, st) → ¬ hasSharing(r0, 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: 20
Proof steps: 55
Used lemmas: hasSharing-array-forward, hasSharing-object-rec,
Used spec theorems:
Used simplifier rules:
- list/references/c-08
- nat-basic2/l
- int-abs/lels-01
- int-abs/lels-04
- int-abs/lels
- int-abs/lels-03
- okfuns/is_array-arraytype
- int-abs/forward-le-01
- int-abs/forward-le-05
- list/references/c-03
- list/references/Nil
- list/references/fr
- list/references/in-08
- list-last/references/last-def
- cyclic/validrefs-sametype
- list/references/len
- list/references/len-02
- nat-basic2/s
- nat-basic1/ref-1
- nat-basic2/a
- nat-basic2/c
- list/references/inapp-07
- list/references/ni
- addfuns/is_obj-classtype
- list/references/c-05
- javavalue/test-19
- javavalue/elim-13
- list/references/in-17
- list/references/in-append
- list/references/in-14
- list/references/in-15
- fieldspec/elim
- cyclic/validrefs-not
- list/references/e
- list/references/app-02-ant
- cyclic/validrefs-null-02
- typefuns/ref
- list/references/e-02
- list-last/references/last-elim
- list-last/references/l-02
- list/references/app
- list-last/references/l
- list/references/a
- list/references/e-01
- list/references/c
- list-data/references/elim-list-c