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Theorem multi-length-first
⊦ # refs + 1 = i→n(countrefs(i ' + ints .rest)) ∧ ints ≠ [] ∧ 0 ≤ i ∧ posints(ints) ∧ ¬ 0 ∈ ints .butlast ∧ i ≤ ints .first ∧ n→i(# acc) + i = ints .first → (addmultiarrays(r ' + refs, i, acc, ty, ints, st)[r -- _length]) = intval(ints .first)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
addarrays-length
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 10
Proof steps: 29
Used lemmas:
countrefs-zero
,
countrefs-rec-02
,
countrefs-not-zero-01
,
countrefs-i2n
,
countrefs-rec-01
,
addmultiarrays-rec
,
addmultiarrays-done
,
addmultiarrays-base
,
Used spec theorems:
list-del
/references/
firstN-rec-01
valuesfuns
/
posints-rec
Used simplifier rules:
int-abs
/
numleledel-01
int-abs
/
numle-02
int-basic2
/
add-in
intnat
/
nat2int-06
int-basic2
/
ls
list
/intlista/
in-10
list-last
/intlista/
bin
int-abs
/
lels-04
int-abs
/
lels-01
list
/intlista/
e
list
/intlista/
app-02-ant
nat-mult
/
coef-18
nat
/
lep-01
nat
/
lels
list-del
/references/
first-length
nat
/
elim-pred-c
nat
/
pred-03
nat
/
eq-01
list-del
/references/
firstN-zero
list
/references/
in-17
list
/references/
in-append
list
/references/
in-14
list-del
/references/
lastN-empty
intnat
/
abs-zero
list-data
/references/
elim-list-c
nat-basic2
/
eq-01
int-mult
/
commutativity
int-mult
/
associativity
nat-mult
/
mult-c
nat-mult
/
mult-a
nat-mult
/
rsucc-02
intnat
/
rax-04
int-abs
/
mone-06
int-abs
/
numls-02
int-abs
/
numadd-01
int-abs
/
elim-sub
list
/references/
c
list
/intlista/
c-07
list
/references/
len-02
list
/references/
len
int-abs
/
ax-02
int-abs
/
lels
int-basic1
/
ls-01
nat-basic2
/
oz
nat-basic1
/
one
nat
/
ax-02
list-data
/references/
l
int-basic2
/
ax-04
intnat
/
n2i-add
int-abs
/
numsub
addarray
/
length-1init-01
valuesfuns
/
mkvalsr-len
int-abs
/
forward-le-05
int-abs
/
lels-02
list
/intlista/
in-06
list-last
/intlista/
bapp
nat-basic2
/
one
list
/intlista/
len
list
/intlista/
len-02
nat-basic2
/
one-03
list-data
/intlista/
l
nat-basic2
/
a
nat-basic2
/
c
list
/references/
c-08
list
/references/
a
list
/intlista/
c-08
addarray
/
length-1dim
javavalue
/
inj-04
valuesfuns
/
posints-rec
list
/intlista/
a
list
/intlista/
e-01
list
/intlista/
c
list-data
/intlista/
elim-list-c
int-abs
/
forward-le-01
intnat
/
nat2int-01
int-basic2
/
add-c
int-basic2
/
add-a