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LeanPool
.
ParameterFreeGradient
.
V7
.
Proofs
.
Stage4AboveTwo
.
Constants
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Imports
Init
LeanPool.ParameterFreeGradient.V7.Proofs.Stage4AboveTwo.Geometry
Imported by
V7
.
Stage4AboveTwo
.
uniformConstant_pos
V7
.
Stage4AboveTwo
.
errorPower_gt_one
V7
.
Stage4AboveTwo
.
errorConstant_pos
V7
.
Stage4AboveTwo
.
budgetConstant_pos
V7
.
Stage4AboveTwo
.
budgetExponent_pos
V7
.
Stage4AboveTwo
.
budgetExponent_lt_one
V7
.
Stage4AboveTwo
.
errorPower_mul_budgetExponent
V7
.
Stage4AboveTwo
.
growthConstant_pos
V7
.
Stage4AboveTwo
.
hpConstant_pos
V7
.
Stage4AboveTwo
.
conjugate_pos
V7
.
Stage4AboveTwo
.
jpConstant_pos
V7
.
Stage4AboveTwo
.
gamma_pos
Positivity of the constants and scales used by the above-two phases.
source
theorem
V7
.
Stage4AboveTwo
.
uniformConstant_pos
{
p
:
ℝ
}
(
hp
:
2
<
p
)
:
0
<
aboveUniformConstant
p
source
theorem
V7
.
Stage4AboveTwo
.
errorPower_gt_one
{
p
:
ℝ
}
(
hp
:
2
<
p
)
:
1
<
aboveErrorPower
p
source
theorem
V7
.
Stage4AboveTwo
.
errorConstant_pos
{
p
:
ℝ
}
(
hp
:
2
<
p
)
:
0
<
aboveErrorConstant
p
source
theorem
V7
.
Stage4AboveTwo
.
budgetConstant_pos
{
p
:
ℝ
}
(
hp
:
2
<
p
)
:
0
<
aboveBudgetConstant
p
source
theorem
V7
.
Stage4AboveTwo
.
budgetExponent_pos
{
p
:
ℝ
}
(
hp
:
2
<
p
)
:
0
<
aboveBudgetExponent
p
source
theorem
V7
.
Stage4AboveTwo
.
budgetExponent_lt_one
{
p
:
ℝ
}
(
hp
:
2
<
p
)
:
aboveBudgetExponent
p
<
1
source
theorem
V7
.
Stage4AboveTwo
.
errorPower_mul_budgetExponent
{
p
:
ℝ
}
(
hp
:
2
<
p
)
:
aboveErrorPower
p
*
aboveBudgetExponent
p
=
1
source
theorem
V7
.
Stage4AboveTwo
.
growthConstant_pos
{
p
:
ℝ
}
(
hp
:
2
<
p
)
:
0
<
aboveGrowthConstant
p
source
theorem
V7
.
Stage4AboveTwo
.
hpConstant_pos
{
p
:
ℝ
}
(
hp
:
2
<
p
)
:
0
<
aboveHp
p
source
theorem
V7
.
Stage4AboveTwo
.
conjugate_pos
{
p
:
ℝ
}
(
hp
:
2
<
p
)
:
0
<
conjugateExponent
p
source
theorem
V7
.
Stage4AboveTwo
.
jpConstant_pos
{
p
:
ℝ
}
(
hp
:
2
<
p
)
:
0
<
aboveJp
p
source
theorem
V7
.
Stage4AboveTwo
.
gamma_pos
{
p
eta
:
ℝ
}
{
n
:
ℕ
}
(
hp
:
2
<
p
)
(
heta
:
0
<
eta
)
(
hn
:
1
≤
n
)
:
0
<
aboveGamma
p
eta
n