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Theorem putarray-addarray-override
⊦ 0 ≤ i ∧ i + n→i(# vals) ≤ n→i(# vals0) → putArray(vals, r, i, addarray(r, ty, vals0, st)) = addarray(r, ty, firstn(i→n(i), vals0) + vals + restn(i→n(i) + # vals, vals0), 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: 67
Proof steps: 137
Used lemmas:
lookup-1init
,
lookup-init
,
type-1init
,
length-1init-01
,
add-at-other
,
add-at-gr
,
add-at-ok-01
,
add-at-other-index
,
add-at-ok
,
length-init
,
in-1init-02
,
in-init-09
,
add-in
,
add-in-other
,
in-init-06
,
in-add
,
in-init-01
,
Used spec theorems:
store
/javastore/
Extension
storearrays
/
putArray-in
intnat
/
num-i2n-le-02
storekey
/
ex-04
intnat
/
num-n2i-ls-06
storearrays
/
putar-atref
intnat
/
num-n2i-ls-02
intnat
/
num-i2n-eq-01
intnat
/
num-i2n-eq
intnat
/
num-n2i-ls-04
list-del
/javavalues/
get-append-less
intnat
/
ls-int-ls-nat
nat-basic2
/
c
nat-basic2
/
a
list-del
/javavalues/
restn-at
list-del
/javavalues/
get-firstn
intnat
/
num-i2n-ls-02
storearrays
/
at=get
storearrays
/
get-get
storearrays
/
putar-at
storearrays
/
putar-atother
storekey
/
ex-03
list-del
/javavalues/
rest-len
intnat
/
le-int-le-nat
Used simplifier rules:
intnat
/
inj
javavalue
/
inj-04
javavalue
/
inj-09
storekey
/
test-05
storekey
/
test-07
storearrays
/
putarray-field
intnat
/
inni-le
int-basic1
/
ls-01
int-abs
/
lels-02
intnat
/
abs-zero
int-abs
/
abs-16
nat
/
lep
int-abs
/
le-add
intnat
/
le
nat
/
lels
int-abs
/
sub-add
intnat
/
n2n
list-del
/javavalues/
get-append-less
int-abs
/
negeq
int-basic2
/
ax-04
int-abs
/
sub-ls-01
int-abs
/
sub-add-06
int-abs
/
sub-add-01
intnat
/
nat2int
int-abs
/
lep
intnat
/
labs-01
nat
/
elim-sub
int-abs
/
absle
intnat
/
labs
list-del
/javavalues/
get-append-grt
int-abs
/
zero-gels-03
nat
/
ls-le-simp
intnat
/
nat2int-04
nat-basic1
/
ref-1
storearrays
/
putArray-at-in
int-abs
/
forward-lele
int-basic2
/
ls-01
specialkeys
/
len
specialkeys
/
length-04
specialkeys
/
type-03
storefuns
/
instore-01
specialkeys
/
type-04
specialkeys
/
type-06
storekey
/
test
intnat
/
add-nonneg-int-to-nat
int-abs
/
zero-gels
int-abs
/
forward-le-05
int-basic2
/
ls
intnat
/
nat2int-08
nat
/
let
int-abs
/
lels-03
int-abs
/
zero-gels-01
int-abs
/
forward-lsle
int-abs
/
forward-lels
int-abs
/
forward-le-02
int-basic2
/
ls-02
intnat
/
num-n2i-ls-02
nat-basic1
/
z
list-data
/javavalues/
l
int-abs
/
lels-04
nat
/
le-ls-simp
list-del
/javavalues/
rest-len
intnat
/
n2i-sub
int-abs
/
Sub-def
int-abs
/
ax-01
int-abs
/
zero-gels-04
nat-basic1
/
f
nat
/
lels-01
int-abs
/
lels
nat-basic2
/
c
nat-basic2
/
a
intnat
/
i2i-pos-01
intnat
/
n2i-add
list
/javavalues/
a
list-del
/javavalues/
first-length
list
/javavalues/
len
int-abs
/
lels-01
storekey
/
test-08
storekey
/
elim-04
int-basic2
/
add-c
int-basic2
/
add-a
refkey
/
sel-02
refkey
/
sel-01
int-abs
/
forward-le-01