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Theorem lagrange-lemma
prime(j), j ≠ 2 ⊦ ∃ i, i0, j0. 1 + i ^2 + i0 ^2 = j0 * j ∧ 0 < j0 ∧ j0 < j
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
lagrange-lemma-smallest
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 37
Proof steps: 52
Used lemmas:
congmod-def
,
congmod-def-mod
,
diff-primes-neg
,
diff-primes
,
diff-primes-dups
,
Used spec theorems:
list-set
/intlista/
dups-app
list-set
/intlista/
filter-empty-def
intlist
/
countFun-in
int-gcd
/
divides-minus
int-gcd
/
divides
int-square
/
Square-def
int-div
/
divmult
int-abs
/
forward-lele
int-abs
/
succ-01
int-mult
/
ls-pos
int-div
/
num-ls
int-mult
/
ls-same-01
int-abs
/
estimate-add1-le-left
int-square
/
le
int-basic2
/
pls-01
Used simplifier rules:
int-div
/
div-two-zero-01
int-gcd
/
prime-not-neg-01
int-abs
/
forward-le-05
int-gcd
/
div-abs-02
int-abs
/
sub-sub
int-abs
/
minus-neg
int-abs
/
forward-le
int-abs
/
forward-le-01
int-mult
/
ls-pos
int-mult
/
le-pos
int-abs
/
succ-01
int-mult
/
square-le
int-abs
/
lep-01
int-abs
/
bet
int-mult
/
one-01
int-abs
/
sub-eq-01
int-abs
/
anti
oelem
/intlista/
lel
int-square
/
zero-i
int-gcd
/
prime-one
int-gcd
/
prime-odd-01
int-abs
/
sub-le-01
int-abs
/
leone
int-abs
/
sub-ls-01
int-abs
/
le-add
int-mult
/
add-mult-two
int-abs
/
int-simp-09
int-mult
/
numle-08
int-mult
/
one
int-abs
/
absle
int-div
/
abs
int-abs
/
abs-09
int-abs
/
abs-16
int-abs
/
zero-gels-04
int-abs
/
forward-le-04
int-abs
/
forward-lele
int-abs
/
forward-lels
int-abs
/
lels
int-mult
/
zero-le
int-abs
/
lels-01
int-abs
/
lenls
int-mult
/
associativity
int-mult
/
commutativity
int-abs
/
zero-gels-01
int-abs
/
forward-le-02
int-abs
/
forward-lsle
oelem
/intlista/
transitivity
int-basic2
/
add-c
int-basic2
/
add-a
int-abs
/
mone-05
int-abs
/
numle-03
int-square
/
two-not-neg