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Theorem prime-product
primes(ints), max(ints) ≤ i, ¬ dups(ints) ⊦ Π ints ≤ 4 ^ i
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
bertrand-middle-primes
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 21
Proof steps: 36
Used lemmas:
prime-product-between
,
Used spec theorems:
int-min
/
odd-def
intlist
/
divide-list-at-value
intlist
/
product-divide
intnat
/
num-i2n-le
int-pot
/
pot-dist-pos
int-mult
/
ple-pos-better
int-basic1
/
ls-rec
int-min
/
odd-even-rew
int-pot
/
Pot-pos
Used simplifier rules:
int-abs
/
lenls
int-abs
/
forward-lele
intlist
/
primes-le-2
list
/intlista/
e
intlist
/
primes-one
int-gcd
/
prime-two-01
intlist
/
max-one
intlist
/
product-one
list-dup
/intlista/
c
int-basic1
/
numlslsdel-01
int-abs
/
forward-le-01
int-div
/
nummult-ls-02
int-mult
/
zero-ge
int-abs
/
mone-06
int-abs
/
numls-02
intlist
/
primes-perm-01
intlist
/
primes-perm-02
list-perm
/intlista/
perm-dups-02
list-perm
/intlista/
perm-dups-03
intlist
/
max-empty
int-abs
/
zero-gs
nat
/
lels
intnat
/
abs-succ-03
int-mult
/
zero-ge-add
intnat
/
n2i-add
intnat
/
i2i-pos
nat-basic2
/
a
nat-basic2
/
c
int-abs
/
le-add
int-mult
/
le-same
int-abs
/
numle-02
int-abs
/
numleledel-01
int-mult
/
add-mult-two
int-abs
/
zero-gels-04
intlist
/
primes-product-not-neg
int-basic2
/
ls-01
oelem
/intlista/
transitivity
intlist
/
max-perm-ls
int-basic1
/
ls-01
int-pot
/
pot-zero-01
int-pot
/
pot-lez
int-abs
/
lsone
int-abs
/
lels-01
int-abs
/
numsub
int-abs
/
succ-02
intlist
/
prod-empty
int-mult
/
one
int-abs
/
leone
list
/intlista/
Nil
list
/intlista/
a
list-dup
/intlista/
e-01
int-abs
/
forward-lsle
int-basic2
/
ls
int-abs
/
forward-lels
oelem
/intlista/
irreflexivity
int-abs
/
sub-le-01
int-abs
/
succ-01
int-basic2
/
add-a
int-basic2
/
add-c
int-abs
/
lels
int-abs
/
anti
intlist
/
primes-max-even
int-abs
/
ler
oelem
/intlista/
lel
int-abs
/
forward-le-05
int-basic1
/
forward-pos
intnat
/
abs-pred
int-abs
/
lels-03
int-abs
/
sub-pred
int-mult
/
numls-07
int-mult
/
zero-gr-01
int-pot
/
notneg-02
int-mult
/
associativity
int-mult
/
commutativity