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Verification
.
Nelsen17UpperLimit
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Imports
Init
Verification.Nelsen17Tails
Mathlib.Analysis.SpecificLimits.Basic
Imported by
Verification
.
n17_diagonal_lower_bound
Verification
.
nelsen17_cdf_lower_bound
Verification
.
nelsen17_tendsto_atTop
← Mathematical handbook
source
theorem
Verification
.
n17_diagonal_lower_bound
{
θ
:
ℝ
}
(
hθ
:
1
≤
θ
)
(
t
:
↑
unitInterval
)
:
(
1
+
↑
t
)
*
4
^
(
-
θ
⁻¹
)
-
1
≤
(
nelsen17
θ
⋯
)
.
diagonal
t
source
theorem
Verification
.
nelsen17_cdf_lower_bound
{
θ
:
ℝ
}
(
hθ
:
1
≤
θ
)
(
u
v
:
↑
unitInterval
)
:
(
1
+
min
↑
u
↑
v
)
*
4
^
(
-
θ
⁻¹
)
-
1
≤
(
nelsen17
θ
⋯
)
.
cdf
![
u
,
v
]
source
theorem
Verification
.
nelsen17_tendsto_atTop
{
α
:
Type
u_1}
{
l
:
Filter
α
}
(
θ
:
α
→
ℝ
)
(
hθ
:
∀ (
a
:
α
),
θ
a
≠
0
)
(
ht
:
Filter.Tendsto
θ
l
Filter.atTop
)
(
u
v
:
↑
unitInterval
)
:
Filter.Tendsto
(fun (
a
:
α
) =>
(
nelsen17
(
θ
a
)
⋯
)
.
cdf
![
u
,
v
]
)
l
(
nhds
(
(
ProbabilityTheory.Copula.comonotonic
2
)
.
cdf
![
u
,
v
]
)
)