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Theorem Binom-theorem-countFun
⊦ 0 ≤ j → (i + i0) ^ j = Σ countFun(0, j, λ j0. binom_coef(j, j0) * i ^ j0 * i0 ^ (j - j0))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Binom-theorem
,
coef-le-2pot
,
middle-coef-larger-strongest
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 26
Proof steps: 43
Used lemmas:
countFun-shift
,
countFun-pot-01
,
countFun-pot
,
countFun-add
,
coef-same
,
coef-zero
,
Used spec theorems:
intlist
/
countFun-base
intlist
/
countFun-dist
int-mult
/
dist-lsplit
intlist
/
countFun-rec
int-mult
/
dist-rsplit
int-pot
/
Pot-pos
intlist
/
countFun-last
intlist
/
countFun-mult
Used simplifier rules:
int-abs
/
lels-02
int-abs
/
sub-pred
int-abs
/
elim-sub
int-abs
/
forward-le-01
int-abs
/
numadd-01
intnat
/
rax-04
nat-basic2
/
s
intnat
/
labs
int-abs
/
absle
oelem
/intlista/
irreflexivity
nat-basic2
/
a
nat-basic2
/
c
int-abs
/
lels-01
int-abs
/
lenls
int-abs
/
zero-gels-04
int-abs
/
mone-06
int-abs
/
numls-02
int-abs
/
sub-add-05
int-basic2
/
add-zero
int-abs
/
numsub
int-abs
/
numleledel-01
int-abs
/
numle-02
int-basic2
/
eq
int-pot
/
one
intlist
/
countFun-one
int-abs
/
neg-06
int-abs
/
anti
int-abs
/
lels
intlist
/
sum-empty
int-abs
/
forward-le-05
int-abs
/
leone
intlist
/
sum-rec
int-abs
/
sub-zero-01
int-basic2
/
add-in
int-basic2
/
pred
int-basic2
/
zero-02
int-mult
/
eq-dist
list
/intlista/
a
intlist
/
sum-one
intlist
/
sum-app
int-mult
/
one
int-pot
/
Pot-zero
int-abs
/
sub-sub-03
int-basic2
/
add-a
int-basic2
/
add-c
int-abs
/
sub-sub-04
int-mult
/
associativity
int-mult
/
commutativity