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Proofgold Proof
pf
Claim L0:
∀ x0 .
...
⟶
∀ x1 .
...
⟶
∀ x2 x3 :
ι →
ι → ι
.
...
⟶
...
⟶
(
λ x4 x5 .
λ x6 :
ι →
ι → ι
.
02a50..
(
0ac37..
(
94f9e..
(
ac767..
(
23e07..
x4
)
(
23e07..
x5
)
)
(
λ x7 .
bc82c..
(
x6
(
f482f..
x7
4a7ef..
)
x5
)
(
bc82c..
(
x6
x4
(
f482f..
x7
(
4ae4a..
4a7ef..
)
)
)
(
f4dc0..
(
x6
(
f482f..
x7
4a7ef..
)
(
f482f..
x7
(
4ae4a..
4a7ef..
)
)
)
)
)
)
)
(
94f9e..
(
ac767..
(
5246e..
x4
)
(
5246e..
x5
)
)
(
λ x7 .
bc82c..
(
x6
(
f482f..
x7
4a7ef..
)
x5
)
(
bc82c..
(
x6
x4
(
f482f..
x7
(
4ae4a..
4a7ef..
)
)
)
(
f4dc0..
(
x6
(
f482f..
x7
4a7ef..
)
(
f482f..
x7
(
4ae4a..
4a7ef..
)
)
)
)
)
)
)
)
(
0ac37..
(
94f9e..
(
ac767..
(
23e07..
x4
)
(
5246e..
x5
)
)
(
λ x7 .
bc82c..
(
x6
(
f482f..
x7
4a7ef..
)
x5
)
(
bc82c..
(
x6
x4
(
f482f..
x7
(
4ae4a..
4a7ef..
)
)
)
(
f4dc0..
(
x6
(
f482f..
x7
4a7ef..
)
(
f482f..
x7
(
4ae4a..
4a7ef..
)
)
)
)
)
)
)
(
94f9e..
(
ac767..
(
5246e..
x4
)
(
23e07..
x5
)
)
(
λ x7 .
bc82c..
(
x6
(
f482f..
x7
4a7ef..
)
x5
)
(
bc82c..
(
x6
x4
(
f482f..
x7
(
4ae4a..
4a7ef..
)
)
)
(
f4dc0..
(
x6
(
f482f..
x7
4a7ef..
)
(
f482f..
x7
(
4ae4a..
4a7ef..
)
)
)
)
)
)
)
)
)
x0
x1
x2
=
(
λ x4 x5 .
λ x6 :
ι →
ι → ι
.
02a50..
...
...
)
...
...
...
...
Apply unknownprop_0d078a833e20a13be15691da098ab7e638a79d34f684fe40cbe56431440f9e3e with
λ x0 x1 .
λ x2 :
ι →
ι → ι
.
02a50..
(
0ac37..
(
94f9e..
(
ac767..
(
23e07..
x0
)
(
23e07..
x1
)
)
(
λ x3 .
bc82c..
(
x2
(
f482f..
x3
4a7ef..
)
x1
)
(
bc82c..
(
x2
x0
(
f482f..
x3
(
4ae4a..
4a7ef..
)
)
)
(
f4dc0..
(
x2
(
f482f..
x3
4a7ef..
)
(
f482f..
x3
(
4ae4a..
4a7ef..
)
)
)
)
)
)
)
(
94f9e..
(
ac767..
(
5246e..
x0
)
(
5246e..
x1
)
)
(
λ x3 .
bc82c..
(
x2
(
f482f..
x3
4a7ef..
)
x1
)
(
bc82c..
(
x2
x0
(
f482f..
x3
(
4ae4a..
4a7ef..
)
)
)
(
f4dc0..
(
x2
(
f482f..
x3
4a7ef..
)
(
f482f..
x3
(
4ae4a..
4a7ef..
)
)
)
)
)
)
)
)
(
0ac37..
(
94f9e..
(
ac767..
(
23e07..
x0
)
(
5246e..
x1
)
)
(
λ x3 .
bc82c..
(
x2
(
f482f..
x3
4a7ef..
)
x1
)
(
bc82c..
(
x2
x0
(
f482f..
x3
(
4ae4a..
4a7ef..
)
)
)
(
f4dc0..
(
x2
(
f482f..
x3
4a7ef..
)
(
f482f..
x3
(
4ae4a..
4a7ef..
)
)
)
)
)
)
)
(
94f9e..
(
ac767..
(
5246e..
x0
)
(
23e07..
x1
)
)
(
λ x3 .
bc82c..
(
x2
(
f482f..
x3
4a7ef..
)
x1
)
(
bc82c..
(
x2
x0
(
f482f..
x3
(
4ae4a..
4a7ef..
)
)
)
(
f4dc0..
(
x2
(
f482f..
x3
4a7ef..
)
(
f482f..
x3
(
4ae4a..
4a7ef..
)
)
)
)
)
)
)
)
.
The subproof is completed by applying L0.
■