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Theorem bertrand-estimate
i ≥ 1024 ⊦ ¬ 4 ^ i ≤ 4 ^ ((2 * i) / 3) * (2 * i) ^ sqrt(2 * i)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
BertrandsPostulate
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 10
Proof steps: 15
Used lemmas:
Used spec theorems:
int-div
/
div-mult-nle-est
int-pot
/
pot-div
int-pot
/
pot-root-est
int-pot
/
le-pos
int-mult
/
dist-lsplit
int-div
/
div-add1-pospos
Used simplifier rules:
int-abs
/
forward-le
int-abs
/
lels
int-abs
/
ge-def
int-pot
/
notneg-02
int-div
/
div-mult-nls-zero
int-pot
/
grz
int-abs
/
lenls
int-div
/
pos
int-basic2
/
ls-02
int-abs
/
forward-lels
int-abs
/
lels-01
int-abs
/
sub-le-01
int-div
/
div-elim-pospos
int-basic1
/
numlslsdel-01
int-mult
/
ls-pos
int-abs
/
forward-lele
int-basic1
/
forward-pos
int-abs
/
forward-le-05
int-abs
/
forward-le-01
int-abs
/
forward-lsle
int-mult
/
zero-ge-add
int-mult
/
numls-03
int-mult
/
associativity
int-mult
/
commutativity
int-div
/
mod-zero-num
int-mult
/
zero-ge
int-abs
/
zero-gels-04
int-div
/
div-mult-num
int-mult
/
numsucc
int-basic2
/
add-a
int-basic2
/
add-c
int-basic2
/
ls-01
int-div
/
nls-mult-div