[Imprint]
[Data Privacy Statement]
[E-Mail]
View
long theorem info
. View
the proof
. Back to
main index
. View
the specification
. View
theorem base summary
, View
theorem base listing
, the
used properties by spec
, the
dependency list
, the
symbol table
,
Theorem diff-primes-neg
⊦ prime(j) ∧ j ≠ 2 → ¬ dups(countFun(0, (j - 1) / 2, λ i. (~1 - i ^2) |%| j))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
lagrange-lemma
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 24
Proof steps: 41
Used lemmas:
congmod-def
,
congmod-def-mod
,
Used spec theorems:
list-del
/intlista/
dups-def
intlist
/
countFun-length
intlist
/
countFun-at
intnat
/
num-i2n-ls-02
int-gcd
/
prime-divides
int-gcd
/
div-not-ls
int-div
/
divmult
int-abs
/
estimate-add1-le-right
int-abs
/
notle-pos
int-gcd
/
div-mod
int-div
/
mod-zero-05
int-square
/
Square-def
int-mult
/
dist-sub-split
int-mult
/
dist-rsplit
Used simplifier rules:
list-data
/intlista/
l
int-gcd
/
prime-not-neg
int-abs
/
numle-02
int-abs
/
lels-02
int-abs
/
mone-06
int-abs
/
succ-02
int-abs
/
lels-03
int-div
/
div-ls-mone
int-abs
/
numsub
int-abs
/
numle-03
int-abs
/
forward-le-03
nat-basic2
/
succ
nat-basic1
/
trans-1
nat-basic1
/
f
nat-basic1
/
lf
intnat
/
nat2int-04
int-abs
/
sub-zero-01
int-abs
/
anti
intlist
/
countFun-one
int-square
/
zero-i
list
/intlista/
e
int-gcd
/
div-abs-02
int-abs
/
sub-sub-04
int-abs
/
minus-add
int-abs
/
sub-sub
nat
/
lels
nat-basic2
/
c
nat-basic2
/
a
nat-basic2
/
s
intnat
/
abs-succ-03
int-mult
/
zero-gr
int-mult
/
zero-ge
int-gcd
/
prime-odd-01
int-abs
/
lep-01
int-mult
/
add-mult-two
int-abs
/
lels-01
int-basic2
/
ls-01
int-abs
/
lenls
int-abs
/
forward-le-04
int-abs
/
forward-lels
intnat
/
nat2int-10
nat-basic1
/
lf-02
intnat
/
abs-zero
int-abs
/
numadd-01
int-div
/
div-two-zero-01
int-abs
/
sub-le-01
int-abs
/
zero-gels-04
int-basic2
/
add-zero
int-basic1
/
forward-pos
int-abs
/
forward-le-05
nat-basic1
/
one
int-div
/
mod-less-01
oelem
/intlista/
lel
intnat
/
inj
intnat
/
abs-02
int-abs
/
lels
int-abs
/
forward-lele
int-abs
/
forward-le-01
int-abs
/
forward-le
int-abs
/
forward-lsle
intnat
/
nat2int
intnat
/
num-n2i-ls-02
nat-basic1
/
zero
int-basic2
/
ls
intnat
/
nat2int-08
int-abs
/
sub-eq
int-abs
/
sub-add-01
int-basic2
/
add-in
int-mult
/
eq-dist
int-basic2
/
add-a
int-basic2
/
add-c
int-mult
/
associativity
int-mult
/
commutativity