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Theorem prime-divides-coef
⊦ j + 2 ≤ j0 ∧ j0 ≤ j * 2 + 1 ∧ prime(j0) ∧ 0 < j → j0 | binom_coef(2 * j + 1, j)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
coef-product-le
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 11
Proof steps: 18
Used lemmas:
prime-fac-divides
,
prime-fac-divides-01
,
prime-fac-divides-not
,
fac-not-zero
,
binom-def
,
fac-divides
,
Used spec theorems:
int-gcd
/
divides
int-div
/
div-mult
int-gcd
/
prime-divides
Used simplifier rules:
int-abs
/
forward-le-05
int-abs
/
forward-le-01
int-basic1
/
ls-01
int-mult
/
numsub
int-abs
/
numleledel-01
int-abs
/
numle-02
int-mult
/
numle-12
int-gcd
/
prime-divides
int-abs
/
forward-lele
int-abs
/
lep-01
int-mult
/
zero-gr
int-abs
/
forward-le
int-basic1
/
forward-pos
int-abs
/
forward-lsle
oelem
/intlista/
transitivity
int-basic2
/
zero-02
int-abs
/
lels
int-abs
/
int-add-pos
int-abs
/
zero-gels-04
int-abs
/
le-add
int-mult
/
le-same-01
int-abs
/
succ-02
int-basic2
/
add-a
int-basic2
/
add-c
int-abs
/
numls-02
int-abs
/
mone-06
int-mult
/
zero-ge
int-mult
/
associativity
int-mult
/
commutativity
int-abs
/
lels-01
int-abs
/
les
int-abs
/
numle-01
int-abs
/
minus-add
int-abs
/
sub-le-01
int-mult
/
numle-08
int-mult
/
one
int-abs
/
leone
int-mult
/
numls-01
int-mult
/
Mult-zero