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Theorem putarray-addarray
⊦ 0 ≤ j ∧ j ≤ i ∧ i ≤ j + n→i(# vals) → putArray(vals, r, j, addarray(r, val, i, st)) = addarray(r, mklist(val, i→n(j)) + vals, 0, st)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
putByteArray-vals-addarray
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 10
Proof steps: 20
Used lemmas:
1dim-01
,
addarray-lastrec
,
addarray-mklist-02
,
Used spec theorems:
storearrays
/
putAr-lastrec
storearrays
/
putArray-put-switch
Used simplifier rules:
nat
/
lels-01
int-basic2
/
ls
intnat
/
nat2int-08
store
/javastore/
insins
nat
/
ler
intnat
/
le
int-abs
/
succ-02
int-basic2
/
ls-01
int-abs
/
numls-02
int-abs
/
forward-le-05
intnat
/
nat2int-13
int-abs
/
les
nat-basic2
/
s
nat-basic1
/
ref-1
int-abs
/
lels-01
int-abs
/
lels-04
int-abs
/
le-add
oelem
/intlista/
irreflexivity
int-abs
/
mone-08
oelem
/intlista/
lel
int-abs
/
forward-lsle
int-abs
/
forward-le-02
int-abs
/
num-between
int-abs
/
mone-06
intnat
/
num-n2i-eq-01
intnat
/
num-n2i-ls-07
int-abs
/
numleledel-01
list
/javavalues/
e-02
int-basic2
/
add-in
list
/javavalues/
len-02
list-last
/javavalues/
last-elim
intnat
/
nat2int-01
int-abs
/
numle-02
int-abs
/
elim-sub
list-last
/javavalues/
lapp
nat-basic2
/
c
nat-basic2
/
a
intnat
/
n2i-add
list-last
/javavalues/
mk-len
list
/javavalues/
len
list-last
/javavalues/
bapp
list
/javavalues/
app-02-ant
list-last
/javavalues/
mk-empty
intnat
/
abs-zero
intnat
/
i2i-pos-01
int-abs
/
ler
int-abs
/
anti
int-abs
/
zero-gels-04
int-basic2
/
ax-04
list-data
/javavalues/
size-01
list
/javavalues/
a
list
/javavalues/
app
storearrays
/
putArray-empty
int-basic2
/
add-c
int-basic2
/
add-a
intnat
/
nat2int
int-abs
/
lep
int-abs
/
forward-le-01
int-abs
/
forward-lele