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Theorem get-add-02
⊦ 0 ≤ i ∧ 0 ≤ j ∧ i + j ≤ n→i(# vals) → getarray(r, i, j, addarray(r, ty, vals, st)) = sublist(i→n(i), i→n(j), vals)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
get-add-01
,
getbar-addbar-02
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 13
Proof steps: 27
Used lemmas:
init-at
,
at-init-01
,
at-init-02
,
addarrayinit-def
,
Used spec theorems:
storearrays
/
getArray-zero
storearrays
/
getArray-rec
storearrays
/
getArray-one
list-del
/javavalues/
sublist-one
intnat
/
num-i2n-le-02
list-del
/javavalues/
sublist-lenrec
intnat
/
num-n2i-ls-02
intnat
/
add-01
Used simplifier rules:
nat-basic1
/
f
list
/javavalues/
a
list
/javavalues/
c-04
list
/javavalues/
app-01
nat
/
le-ls-simp
int-abs
/
forward-le-02
oelem
/intlista/
transitivity
int-basic2
/
ls
int-basic2
/
zero-02
int-abs
/
numls-02
int-basic2
/
ax-04
int-abs
/
numsub
int-abs
/
numadd-01
nat-basic2
/
z
nat
/
add-01
intnat
/
rax
int-abs
/
elim-sub
oelem
/intlista/
irreflexivity
int-abs
/
abs
intnat
/
labs
nat-basic2
/
s
nat
/
ls-01
intnat
/
num-i2n-le-02
nat
/
pred-03
intnat
/
rax-01
int-abs
/
sub-add-01
int-abs
/
sub-le
int-abs
/
sub-le-01
int-abs
/
leone
oelem
/intlista/
sls
int-basic1
/
ls-01
int-abs
/
forward-lsle
intnat
/
nat2int-11
nat-basic2
/
l-02
nat-basic2
/
a
nat-basic2
/
c
int-basic1
/
forward-pos
list
/javavalues/
Last
nat
/
lels
int-abs
/
lels-01
int-abs
/
lels-04
int-abs
/
lels-03
list-data
/javavalues/
l
nat-basic1
/
z
intnat
/
num-n2i-ls-02
int-basic2
/
add-c
int-basic2
/
add-a
int-abs
/
succ-01
int-abs
/
bet
int-abs
/
lels
int-abs
/
forward-le-05
int-abs
/
lels-02
int-abs
/
anti
list-del
/javavalues/
sub-zerolen
int-abs
/
forward-le-01