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Theorem pot-root-est
⊦ 1024 ≤ i → ¬ 4 ^ (i / 3) ≤ (2 * i) ^ sqrt(2 * i)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 31
Proof steps: 33
Used lemmas:
le-pos
,
square-nls
,
pot-square-est
,
pot-square-04
,
notneg-02
,
ls-pos-03
,
pot-pot-02
,
notneg
,
Used spec theorems:
int-square
/
root-elim
int-div
/
div-mult-nle-est
int-mult
/
commutativity
int-square
/
root-le
int-abs
/
forward-lele
int-div
/
ls-03
int-square
/
Sqrt-def
int-square
/
Square-def
int-mult
/
dist-lsplit
Used simplifier rules:
int-abs
/
forward-le
int-abs
/
numls-03
int-abs
/
forward-lele
int-div
/
nummult-le-02
int-abs
/
numleledel-01
int-mult
/
square-gez
int-div
/
zero-03
int-mult
/
zero-ge-02
int-square
/
square-not-neg-04
int-div
/
pos
int-div
/
div-mult-le
int-div
/
div-div-num
int-div
/
num-ls
int-div
/
div-two-zero-01
int-basic1
/
numlsf
int-basic1
/
forward-pos
int-abs
/
forward-le-05
int-abs
/
forward-lels
int-abs
/
lels-03
int-abs
/
lels
int-mult
/
zero-ge
int-abs
/
zero-gels-04
int-basic1
/
lf-01
int-basic1
/
trans
int-abs
/
forward-lsle
int-abs
/
forward-le-02
int-basic2
/
succ-01
int-abs
/
zero-gels-01
int-mult
/
modzero
int-square
/
square-not-neg-03
int-mult
/
one
int-mult
/
associativity
int-mult
/
commutativity
int-basic2
/
add-a
int-abs
/
succ-02
int-abs
/
lels-01
int-basic2
/
add-c
int-basic1
/
lf-02
int-abs
/
forward-le-01
int-mult
/
ls-add-02
int-mult
/
add-mult-two
int-abs
/
lenls