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Theorem primes-divide
¬ dups(ints), ∀ j. j ∈ ints → prime(j) ∧ j | i, 0 < i ⊦ Π ints ≤ i
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: 7
Proof steps: 12
Used lemmas:
Used spec theorems:
int-gcd
/
divides
int-mult
/
ls-pos
int-gcd
/
divides-prime
Used simplifier rules:
intlist
/
prod-empty
int-abs
/
leone
int-abs
/
lels
list
/intlista/
in-17
list
/intlista/
in-append
list-dup
/intlista/
dups-cons
int-abs
/
lels-01
list
/intlista/
a
intlist
/
prod-rec
list
/intlista/
c
int-mult
/
ls-forward
int-div
/
div-mult-03
int-gcd
/
prime-not-neg-01
int-mult
/
Mult-zero
int-basic1
/
lst-01
int-mult
/
ls-neg
int-mult
/
zero-gr-01
int-gcd
/
prime-not-neg
int-basic1
/
forward-pos
int-abs
/
forward-le-05
oelem
/intlista/
transitivity
int-gcd
/
prime-divides
int-abs
/
lels-03
int-mult
/
commutativity
int-mult
/
associativity
int-mult
/
zero-gr
int-gcd
/
prime-abs
oelem
/intlista/
lel
int-abs
/
numlelsdel-01
int-gcd
/
prime-one