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Theorem validrefs-not-contains
⊦ ¬ contains(str, st[refs .first -- _type] .type, st[refs .last -- _type] .type) ∧ refs ≠ [] ∧ refs .first ≠ refs .last ∧ refs .last ≠ jvmref → ¬ validrefs(str, refs, ty, st)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
nopathex-badarrayfield
,
nopathex-runtimetype
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 48
Proof steps: 125
Used lemmas:
contains-rec
,
contains-two
,
contains-type-def
,
Used spec theorems:
cyclic
/
validrefs-one
addfuns
/
is-valid-ref-stronger-def
cyclic
/
validrefs-class
cyclic
/
validrefs-array
cyclic
/
validrefs-is-junk
Used simplifier rules:
addfuns
/
is_obj-arraytype
list
/references/
e-02
list-last
/references/
last-elim
list-last
/references/
l-02
typefuns
/
ref
okfuns
/
is_array-classtype
okfuns
/
is_array-reftype
okfuns
/
is_array-typeex
int-abs
/
forward-le-01
int-abs
/
forward-le-05
addfuns
/
is_obj-no-interface
fieldspec
/
sel-03
addfuns
/
is_valid_ref-typeex
javatype
/
test-28
javatype
/
sel-02
classnamefuns
/
le-reflexive
typefuns
/
subclass
javatype
/
test-10
typefuns
/
class-le
typefuns
/
typeex-class
typefuns
/
reftype-class
addfuns
/
is_obj-classtype
javatype
/
elim-02
addfuns
/
is_obj-reftype
typefuns
/
le-noreftype
addfuns
/
is_obj-typeex
list
/javatypes/
a
list
/javatypes/
Nil
list
/javatypes/
Last
javavalue
/
test-19
javavalue
/
elim-13
fieldspec
/
elim
list
/references/
first
cyclic
/
validrefs-null-02
list
/references/
e
list
/references/
app-02-ant
list-last
/references/
l-05
list
/references/
app
list-last
/references/
l
list-data
/references/
elim-list-c
list
/references/
e-01
list
/references/
a
list
/references/
c-08
list
/references/
c