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Theorem sharing-twopaths

⊦ sks ≠ [] ∧ sks0 ≠ [] ∧ st[r -- sks] .refval ≠ jvmref ∧ st[r -- sks0] .refval ≠ jvmref ∧ r ≠ jvmref ∧ path∃(str, st[r -- sks] .refval, st[r -- sks0] .refval, st) ∧ sks ≠ sks0 ∧ fits(r, sks, st) ∧ fits(r, sks0, st) ∧ ¬ sks ⊑ sks0 → hasSharing(r, 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: 10
Proof steps: 32
Used lemmas: fits-append, ex-validrefs-fits-stronger, hasSharing-def,
Used spec theorems:
- cyclic/pathex-def
- list-del/references/get-last2
- storefuns/lookup-append
Used simplifier rules:
- javavalue/sel-09
- storefuns/lookup-empty
- javavalue/inj-03
- list-data/storekeys/size-01
- list-last/storekeys/prefix-app-05
- list/storekeys/app-04
- list/storekeys/a
- list/storekeys/app-02-ant
- list-del/storekeys/first-all-01
- nat-basic1/ref-1
- list-data/references/l
- nat/lels-01
- nat-basic1/z
- list/references/c-08
- nat-basic2/c
- nat-basic2/a
- nat-basic2/eq-01
- list/references/len-02
- list/references/len
- list/references/app-02-ant
- list/references/e
- list-last/references/l-02
- javavalue/test-19
- valuefuns/refval-xtra
- javavalue/elim-refval
- list-last/references/l
- list/references/app
- list/references/a
- list/references/e-01
- list/references/c
- list-data/references/elim-list-c