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Theorem addarray-put-01
⊦ 0 ≤ i ∧ 0 ≤ j ∧ j < i → (addarray(r, ty, i, st)[r -- j ', val]) = addarray(r, ty, ((j = 0 ⊃ []; mklist(initial_value(ty), i→n(j)))) + (val + mklist(initial_value(ty), i→n(i - j + 1))), 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: 52
Proof steps: 129
Used lemmas:
add-at-04
,
at-1dim
,
at-1dim-other-index
,
add-at-other-index
,
length-1init-01
,
length-1dim
,
type-1init
,
type-1dim
,
at-field-1dim
,
lookup-1init
,
lookup-1dim
,
in-1dim-14
,
in-1dim-16
,
in-1init-02
,
in-1dim-other
,
add-in-other
,
in-1dim-05
,
in-1dim-fskey
,
add-in
,
type-in
,
length-init
,
length-1dim-02
,
add-in-fskey
,
in-init-01
,
in-1dim-01
,
add-at-ok
,
zero-1init-05
,
in-add
,
Used spec theorems:
store
/javastore/
Extension
storekey
/
ex-04
list-del
/javavalues/
get-append-less
intnat
/
num-i2n-le-01
intnat
/
num-i2n-eq-01
intnat
/
num-i2n-eq
list-del
/javavalues/
get-mklist-01
Used simplifier rules:
int-basic2
/
eq
intnat
/
nat2int-07
int-abs
/
le-add
int-abs
/
negeq
int-abs
/
numadd-01
nat
/
le-ls-simp
nat-basic2
/
oz
nat-basic1
/
one-01
nat-basic2
/
z
intnat
/
abs-eq
intnat
/
labs-01
int-abs
/
abs
nat
/
elim-sub
int-basic2
/
zero-02
int-basic2
/
ls-02
oelem
/intlista/
transitivity
int-basic1
/
forward-pos
int-abs
/
absle
intnat
/
nat2int
intnat
/
inni-le
nat
/
lels
intnat
/
abs-zero
nat
/
elim-pred-c
intnat
/
num-i2n-ls
int-abs
/
lsone
int-abs
/
forward-le
int-basic1
/
lst-01
javavalue
/
inj-04
javavalue
/
inj-09
int-abs
/
forward-lsle
storekey
/
sel-06
storekey
/
test-06
storekey
/
inj-04
specialkeys
/
type-03
specialkeys
/
len
storekey
/
test-08
storekey
/
elim-04
int-abs
/
succ-01
int-abs
/
lels
storekey
/
test
storekey
/
test-02
storefuns
/
instore-01
storekey
/
test-01
refkey
/
inj-01
store
/javastore/
At-other
oelem
/intlista/
irreflexivity
int-abs
/
abs-16
intnat
/
labs
list-del
/javavalues/
get-append-grt
nat
/
zero
list-del
/javavalues/
get-zero-01
int-abs
/
zero-gels-04
int-basic1
/
ls-01
intnat
/
i2i-pos
int-abs
/
lels-02
list
/javavalues/
Nil
int-basic2
/
ax-04
list-data
/javavalues/
size-01
int-basic2
/
ls
store
/javastore/
At-same
store
/javastore/
In-insert
nat-basic2
/
c
nat-basic2
/
a
intnat
/
i2i-pos-01
intnat
/
n2i-add
list
/javavalues/
a
list-last
/javavalues/
mk-len
list
/javavalues/
len-02
list
/javavalues/
len
int-abs
/
lels-04
int-abs
/
lels-01
store
/javastore/
insin
int-abs
/
numleledel-01
int-abs
/
mone-06
int-abs
/
numls-02
int-abs
/
numle-02
int-basic2
/
add-c
int-basic2
/
add-a
int-abs
/
lep
int-abs
/
succ-02
int-abs
/
forward-le-01
int-abs
/
forward-le-05
list
/javavalues/
c
int-abs
/
elim-sub