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Proofgold Proof
pf
Let x0 of type
ι
be given.
Assume H0:
1eb0a..
x0
.
Let x1 of type
ι
→
ο
be given.
Assume H1:
∀ x2 x3 x4 x5 x6 x7 x8 x9 .
SNo
x2
⟶
SNo
x3
⟶
SNo
x4
⟶
SNo
x5
⟶
SNo
x6
⟶
SNo
x7
⟶
SNo
x8
⟶
SNo
x9
⟶
x0
=
bbc71..
x2
x3
x4
x5
x6
x7
x8
x9
⟶
x1
(
bbc71..
x2
x3
x4
x5
x6
x7
x8
x9
)
.
Apply H0 with
x1
x0
.
Let x2 of type
ι
be given.
Assume H2:
(
λ x3 .
and
(
SNo
x3
)
(
∃ x4 .
and
(
SNo
x4
)
(
∃ x5 .
and
(
SNo
x5
)
(
∃ x6 .
and
(
SNo
x6
)
(
∃ x7 .
and
(
SNo
x7
)
(
∃ x8 .
and
(
SNo
x8
)
(
∃ x9 .
and
(
SNo
x9
)
(
∃ x10 .
and
(
SNo
x10
)
(
x0
=
bbc71..
x3
x4
x5
x6
x7
x8
x9
x10
)
)
)
)
)
)
)
)
)
x2
.
Apply H2 with
x1
x0
.
Assume H3:
SNo
x2
.
Assume H4:
∃ x3 .
and
(
SNo
x3
)
(
∃ x4 .
and
(
SNo
x4
)
(
∃ x5 .
and
(
SNo
x5
)
(
∃ x6 .
and
(
SNo
x6
)
(
∃ x7 .
and
(
SNo
x7
)
(
∃ x8 .
and
(
SNo
x8
)
(
∃ x9 .
and
(
SNo
x9
)
(
x0
=
bbc71..
x2
x3
x4
x5
x6
x7
x8
x9
)
)
)
)
)
)
)
.
Apply H4 with
x1
x0
.
Let x3 of type
ι
be given.
Assume H5:
(
λ x4 .
and
(
SNo
x4
)
(
∃ x5 .
and
(
SNo
x5
)
(
∃ x6 .
and
(
SNo
x6
)
(
∃ x7 .
and
(
SNo
x7
)
(
∃ x8 .
and
(
SNo
x8
)
(
∃ x9 .
and
(
SNo
x9
)
(
∃ x10 .
and
(
SNo
x10
)
(
x0
=
bbc71..
x2
x4
x5
x6
x7
x8
x9
x10
)
)
)
)
)
)
)
)
x3
.
Apply H5 with
x1
x0
.
Assume H6:
SNo
x3
.
Assume H7:
∃ x4 .
and
(
SNo
x4
)
(
∃ x5 .
and
(
SNo
x5
)
(
∃ x6 .
and
(
SNo
x6
)
(
∃ x7 .
and
(
SNo
x7
)
(
∃ x8 .
and
(
SNo
x8
)
(
∃ x9 .
and
(
SNo
x9
)
(
x0
=
bbc71..
x2
x3
x4
x5
x6
x7
x8
x9
)
)
)
)
)
)
.
Apply H7 with
x1
x0
.
Let x4 of type
ι
be given.
Assume H8:
(
λ x5 .
and
(
SNo
x5
)
(
∃ x6 .
and
(
SNo
x6
)
(
∃ x7 .
and
(
SNo
x7
)
(
∃ x8 .
and
(
SNo
x8
)
(
∃ x9 .
and
(
SNo
x9
)
(
∃ x10 .
and
(
SNo
x10
)
(
x0
=
bbc71..
x2
x3
x5
x6
x7
x8
x9
x10
)
)
)
)
)
)
)
...
.
...
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