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Theorem nonnullrefs-dups
⊦ dups(vals .nonnullrefs) ↔ (∃ r, m, n. vals[m] = refval(r) ∧ vals[n] = refval(r) ∧ r ≠ jvmref ∧ m ≠ n ∧ m < # vals ∧ n < # vals)
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: 18
Proof steps: 50
Used lemmas:
nonnullrefs-in
,
nonnullrefs-yes
,
nonnullrefs-no
,
nonnullrefs-empty
,
Used spec theorems:
list-del
/javavalues/
get-numrec
list-del
/javavalues/
get-rec
Used simplifier rules:
list
/javavalues/
e-01
list
/javavalues/
c-07
list
/javavalues/
app-02-ant
list
/javavalues/
e
javavalue
/
sel-09
nat
/
elim-pred-c
nat
/
pred-03
list-del
/javavalues/
get-zero-01
javavalue
/
inj-03
nat-basic2
/
oz
nat-basic1
/
less-1
list-del
/javavalues/
get-succ
nat-basic2
/
eq-01
nat-basic2
/
s
nat
/
ls-le-simp
list-data
/javavalues/
l
nat-basic1
/
f
javavalue
/
test-19
javavalue
/
elim-13
list
/references/
a
list-dup
/references/
rec
list
/references/
c
nat-basic2
/
c
nat-basic2
/
a
nat
/
succ-01
list
/javavalues/
a
list
/javavalues/
len-02
list
/javavalues/
len
list
/javavalues/
c
nat
/
lels-01
list-dup
/references/
e-01
list-data
/javavalues/
size-01
nat
/
lez
nat
/
lels