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Theorem coef-product-le
∀ i. i ∈ ints → prime(i) ∧ j + 2 ≤ i ∧ i ≤ j * 2 + 1, ¬ dups(ints), 0 < j ⊦ Π ints ≤ binom_coef(2 * j + 1, j)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
prime-product-between
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 6
Proof steps: 12
Used lemmas:
coef-eq-zero
,
coef-le-zero
,
prime-divides-coef
,
primes-divide
,
Used spec theorems:
int-mult
/
ls-add
Used simplifier rules:
int-abs
/
lels-01
int-abs
/
lels-03
int-abs
/
leone
int-mult
/
one
int-mult
/
numle-08
int-abs
/
sub-le-01
int-abs
/
minus-add
int-abs
/
numle-01
int-abs
/
forward-lele
int-abs
/
forward-le-05
oelem
/intlista/
lel
int-basic1
/
ls-01
int-abs
/
lels
int-abs
/
bet
int-mult
/
one-01
int-mult
/
associativity
int-mult
/
commutativity
int-basic2
/
add-a
int-basic2
/
add-c
int-basic1
/
forward-pos