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.
Nelsen18Order
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Imports
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Verification.Nelsen18
Copula.Order.Orthant
Mathlib.Analysis.MeanInequalitiesPow
Imported by
Verification
.
n18Inv_power
Verification
.
n18Psi_power
Verification
.
nelsen18_lowerOrthant_monotone
← Mathematical handbook
source
theorem
Verification
.
n18Inv_power
{
θ
η
:
ℝ
}
(
hθ
:
0
<
θ
)
(
hη
:
0
<
η
)
(
u
:
↑
unitInterval
)
:
n18Inv
η
u
=
n18Inv
θ
u
^
(
η
/
θ
)
source
theorem
Verification
.
n18Psi_power
{
θ
η
t
:
ℝ
}
(
hθ
:
0
<
θ
)
(
hη
:
0
<
η
)
(
ht
:
0
≤
t
)
:
n18Psi
η
(
t
^
(
η
/
θ
))
=
n18Psi
θ
t
source
theorem
Verification
.
nelsen18_lowerOrthant_monotone
{
θ
η
:
ℝ
}
(
hθ
:
2
≤
θ
)
(
hθη
:
θ
≤
η
)
:
(
nelsen18
θ
hθ
)
.
LowerOrthantLE
(
nelsen18
η
⋯
)