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Theorem countFun-shift
⊦ Σ countFun(i2, i1 - 1, λ j0. i * binom_coef(i1, j0) * i ^ j0 * i0 ^ (i1 - j0)) = Σ countFun(i2 + 1, i1, λ j0. i * binom_coef(i1, j0 - 1) * i ^ (j0 - 1) * i0 ^ (i1 - (j0 - 1)))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Binom-theorem-countFun
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 13
Proof steps: 23
Used lemmas:
Used spec theorems:
intlist
/
countFun-rec
int-abs
/
Abs-pos
int-abs
/
Abs-neg
int-mult
/
le-two
intlist
/
countFun-base
Used simplifier rules:
int-abs
/
lels-03
int-abs
/
succ-01
int-basic2
/
add-in
list
/intlista/
a
intlist
/
sum-rec
int-abs
/
sub-sub-04
int-abs
/
abs-03
int-abs
/
lep
int-abs
/
forward-lsle
int-abs
/
lels
int-abs
/
sub-ls-01
int-abs
/
abssub-01
intnat
/
labs
int-abs
/
sub-sub
int-basic2
/
add-less
oelem
/intlista/
transitivity
int-abs
/
Abs-pos
int-abs
/
sub-add-06
int-abs
/
lep-01
int-abs
/
sub-le-01
int-mult
/
add-mult-two
int-abs
/
sub-add-01
int-abs
/
minus-sub
int-abs
/
neg-06
int-basic2
/
lst-02
int-abs
/
numadd
int-abs
/
minus-add
int-abs
/
sub-eq
int-mult
/
eq-dist
int-abs
/
ler
intlist
/
countFun-base-01
int-basic2
/
add-zero
int-abs
/
numsub
oelem
/intlista/
lel
int-abs
/
les
int-basic2
/
ls-01
int-abs
/
sub-ls
intlist
/
sum-empty
int-abs
/
succ-02
int-abs
/
lels-01
int-abs
/
lenls
int-basic2
/
add-a
int-basic2
/
add-c
int-mult
/
associativity
int-mult
/
commutativity