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Theorem nonnullrefs-in-key
⊦ ¬ dups(fis .keys) → (r ∈ fis .vals .nonnullrefs ↔ r ≠ jvmref ∧ (∃ sk. fis[sk] = refval(r) ∧ sk ∈ fis))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
nonnullrefs-dups-key
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 9
Proof steps: 22
Used lemmas:
keys-notin-02
,
getkeys-one
,
getkeys-app
,
getvals-rec-01
,
getvals-empty
,
nonnullrefs-in
,
Used spec theorems:
valuesfuns
/
nonnullrefs-one-no
assoclist
/fieldinit/
assoc-no
Used simplifier rules:
assoclist
/fieldinit/
assoc-yes
javavalue
/
inj-03
javavalue
/
test-19
javavalue
/
elim-13
list
/references/
in-17
valuesfuns
/
nonnullrefs-one-yes
assoclist
/fieldinit/
inone
pair
/fieldinit/
elim
assoclist
/fieldinit/
in-append
list
/storekeys/
a
list-dup
/storekeys/
dups-cons
list
/references/
a
list
/references/
in-append
list
/javavalues/
a
valuesfuns
/
nonnullrefs-append
list
/fieldinit-assoclista/
a
list
/fieldinit-assoclista/
c
valuesfuns
/
nonnullrefs-empty
list
/references/
in-empty
valuesfuns
/
nonnullrefs-null