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Theorem pathex-put-cyclic
⊦ path∃(str, r0, r, st) ∧ fs ' ∈ instfields(st[r -- _type] .type .class) ∧ st[r0 -- _type] .type ≤ fs .type ∧ is_classtype(st[r -- _type] .type) ∧ r ≠ jvmref ∧ r0 ≠ jvmref → cyclic(str, r, st[r -- fs ', refval(r0)])
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: 21
Proof steps: 52
Used lemmas:
validrefs-primtype
,
validrefs-superclass
,
validrefs-put-notin-02
,
validrefs-is-junk
,
validrefs-postfix
,
validrefs-one
,
validrefs-class
,
pathex-one
,
pathex-def-nodups
,
cyclic-def-simple
,
Used spec theorems:
addfuns
/
is_obj-put-samefield-01
typefuns
/
le-noreftype
typefuns
/
le-noreftype-01
Used simplifier rules:
specialkeys
/
length-02
specialkeys
/
length-03
specialkeys
/
type-04
typefuns
/
le-08
typefuns
/
isreftype-01
list
/references/
app-02-ant
addfuns
/
is_valid_ref-reftype
typefuns
/
le-noreftype-01
specialkeys
/
type-neq
valuefuns
/
okval-refval
okfuns
/
oktype-okval
javastore
/
at-other-16
refkey
/
inj-01
refkey
/
inj
specialkeys
/
type-05
specialkeys
/
type-01
typefuns
/
le-11
addfuns
/
instfields-type-01
list
/references/
in-01
list
/references/
in-append
list-dup
/references/
f
list
/references/
e-02
list-last
/references/
last-elim
list-last
/references/
l-02
list
/references/
app
list-last
/references/
l
list
/references/
e-01
list
/references/
c
list-data
/references/
elim-list-c
addfuns
/
is_valid_ref-isobj
javavalue
/
sel-09
store
/javastore/
At-same
javatype
/
sel-02
typefuns
/
transitivity-01
list
/references/
first
list
/references/
e
fieldspec
/
sel-03
okfuns
/
oktype-class
javavalue
/
test-19
specialkeys
/
type-11
addfuns
/
is_valid_ref
okfuns
/
is_array-type-04
classnamefuns
/
le-reflexive
typefuns
/
subclass
list
/references/
c-08
list
/references/
a
list
/references/
in-17
list-dup
/references/
c
list-dup
/references/
dups-cons
javastore
/
at-other-06
typefuns
/
class-le
javatype
/
test-10
javatype
/
elim-02
fieldspec
/
elim