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Theorem putByteArray-vals-addarray-01
⊦ 0 ≤ j ∧ j ≤ i ∧ 0 ≤ i1 ∧ i = j + n→i(# bytes) + i1 → putByteArray(bytes, r, j, addarray(r, byte_type, i, st)) = addarray(r, byte_type, mklist(initial_value(byte_type), i→n(j)) + mkjavavalues(bytes) + mklist(initial_value(byte_type), i→n(i1)), 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: 37
Proof steps: 82
Used lemmas:
addarray-is-putarray-01
,
addarray-is-putarray
,
init-switch
,
addarrayinit-def
,
add-put-switch
,
addarray-def
,
Used spec theorems:
storearrays
/
putByteArray
storearrays
/
putArray-put-switch-02
store
/javastore/
Extension
store
/javastore/
In-insert
storearrays
/
putArray-in
storearrays
/
putArray-at
storekey
/
ex-04
intnat
/
add-01
storearrays
/
putar-at
storearrays
/
putArray-at-in
intnat
/
num-i2n-le-02
list-del
/javavalues/
get-append-less
intnat
/
num-i2n-eq
list-del
/javavalues/
get-append-grt
list-del
/javavalues/
get-mklist-01
storearrays
/
putar-atother
Used simplifier rules:
int-abs
/
abs-16
nat
/
lep
list-del
/javavalues/
get-mklist-01
nat
/
le-ls-simp
int-abs
/
lels-02
intnat
/
abs-zero
nat-basic2
/
l-01
nat
/
fle-01
intnat
/
nat2int
intnat
/
le
int-abs
/
le-add
nat-basic2
/
l
nat-basic1
/
lf-02
intnat
/
labs-01
nat-basic1
/
f
int-abs
/
absle
intnat
/
labs
intnat
/
nat2int-08
nat
/
elim-sub
nat
/
lels
list-del
/javavalues/
get-append-less
nat
/
eq-01
list-del
/javavalues/
get-append-grt
nat-basic2
/
l-02
int-abs
/
sub-zero-01
int-abs
/
elim-sub
int-abs
/
forward-le-05
specialkeys
/
type-03
specialkeys
/
len
storearrays
/
putarray-field
specialkeys
/
type-04
javavalue
/
inj-09
javastore
/
at-other-16
storearrays
/
putar-atref
javastore
/
look-ins
int-abs
/
forward-lels
int-abs
/
forward-lsle
int-abs
/
forward-le-02
int-basic2
/
ls-02
intnat
/
num-n2i-ls-02
nat-basic1
/
z
list-data
/bytelist/
l
int-basic2
/
ls-01
int-basic2
/
ls
int-abs
/
lels-03
storekey
/
test-02
refkey
/
sel-02
refkey
/
sel-01
storekey
/
test-01
refkey
/
inj
store
/javastore/
At-same
javavalue
/
inj-04
refkey
/
inj-01
refkey
/
elim
int-abs
/
lels
int-basic2
/
ax-04
storekey
/
test
storearrays
/
putArray-in
store
/javastore/
In-insert
intnat
/
add-nonneg-int-to-nat
int-abs
/
lels-04
int-abs
/
lels-01
int-abs
/
zero-gs
nat-basic2
/
c
nat-basic2
/
a
intnat
/
i2i-pos-01
intnat
/
n2i-add
list
/javavalues/
a
valuesfuns
/
mkjava-len
list-last
/javavalues/
mk-len
list
/javavalues/
len
specialkeys
/
type-06
specialkeys
/
length-04
int-abs
/
forward-le-01
int-basic2
/
add-c
int-basic2
/
add-a
int-abs
/
lep