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Theorem product-pot-no-dups
∀ i. i ∈ ints → 0 < i ∧ i ^ n→i(#oc(i, ints)) ≤ j ⊦ Π ints ≤ j ^ n→i(# rmdup(ints))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
bertrand-small-primes
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 13
Proof steps: 26
Used lemmas:
product-pot-rec
,
Used spec theorems:
int-pot
/
succ
int-pot
/
ls-pos
int-abs
/
le-rec
int-mult
/
pls-pos-02
int-mult
/
ls-pos-01
Used simplifier rules:
list
/intlista/
in-08
list-data
/intlista/
elim-list-c
list
/intlista/
in-17
list
/intlista/
in-append
list-del
/intlista/
del-y
intnat
/
n2i-add
list-perm
/intlista/
ocappend
list
/intlista/
e-01
list
/intlista/
c
list
/intlista/
len
list
/intlista/
len-02
nat-basic2
/
s
list-del
/intlista/
del-length
nat-basic2
/
a
nat-basic2
/
c
int-abs
/
forward-le-05
list-perm
/intlista/
one
list-del
/intlista/
in-del-new
list-perm
/intlista/
one-01
int-basic2
/
add-zero
list-perm
/intlista/
ocs-del-length
int-abs
/
succ-02
intnat
/
le
list-del
/intlista/
del-rmdup-length-nle
intnat
/
nat2int
int-abs
/
forward-lele
int-pot
/
pot-lez
int-pot
/
pot-zero-01
intnat
/
nat2int-06
int-basic2
/
add-a
int-basic2
/
add-c
int-pot
/
one-01
int-mult
/
commutativity
int-mult
/
associativity
int-mult
/
ls-forward
int-abs
/
forward-le-01
int-pot
/
notneg-02
int-abs
/
forward-lels
int-abs
/
forward-le-02
oelem
/intlista/
transitivity
int-abs
/
lels-01
int-basic1
/
lst-01
list
/intlista/
a
intlist
/
product-min-nlz
int-abs
/
forward-le-04
int-abs
/
lels
intlist
/
min-in
int-abs
/
lenls
intlist
/
min-empty
list-dup
/intlista/
rmdup-e
list-data
/intlista/
size-01
int-pot
/
Pot-zero
intlist
/
prod-empty