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Theorem pathex-put-nopathex
⊦ ¬ path∃(str, r, r0, st) ∧ ¬ junkref(str, r, st) ∧ sk ≠ _type → (path∃(str, r, r1, st[r0 -- sk, val]) ↔ path∃(str, r, r1, 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: 64
Proof steps: 144
Used lemmas:
validrefs-sametype
,
pathex-array
,
validrefs-array
,
pathex-null
,
pathex-class
,
validrefs-null-02
,
validrefs-sametype-03
,
pathex-one
,
validrefs-class
,
validrefs-null
,
validrefs-is-junk
,
pathex-def-simple
,
Used spec theorems:
addfuns
/
is_valid_ref-reftype
addfuns
/
is-valid-ref-stronger-def
junkrefs
/
junkref-class-01
addfuns
/
is_valid_ref-put-01
junkrefs
/
junkref-array
okfuns
/
is_array-put-01
store
/javastore/
At-other
Used simplifier rules:
specialkeys
/
type-03
addfuns
/
is_valid_ref-reftype
addfuns
/
is_valid_ref-put-01
addfuns
/
is_valid_ref-isarray
int-abs
/
lels-03
int-abs
/
lels-04
int-abs
/
lels
int-abs
/
lels-01
okfuns
/
is_array-put-01
javastore
/
look-ins
javastore
/
at-other-18
specialkeys
/
type-04
int-abs
/
forward-le-01
int-abs
/
forward-le-05
junkrefs
/
junkref-noreftype
typefuns
/
le-noreftype-01
junkrefs
/
junkref-null
addfuns
/
is_valid_ref-isobj
javavalue
/
sel-09
fieldspec
/
sel-03
list
/references/
c-08
list
/references/
app-02-ant
list
/references/
e
list
/references/
len
list
/references/
len-02
nat-basic2
/
s
nat-basic1
/
ref-1
nat-basic2
/
a
nat-basic2
/
c
addfuns
/
is_obj-put-01
refkey
/
inj-01
refkey
/
inj
store
/javastore/
At-same
javavalue
/
test-19
javavalue
/
elim-13
fieldspec
/
elim
list-last
/references/
l-02
junkrefs
/
junkref-not-valid-01
list
/references/
app
list-last
/references/
l
typefuns
/
ref
list
/references/
a
list
/references/
e-01
list
/references/
c
list-data
/references/
elim-list-c
javastore
/
at-other-16