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Proofgold Asset
asset id
1178f2a525faba043ca1512d0d08bace3db1eb0e15ac1aa86b0471806cb2140c
asset hash
8b41730a988544b043d56ff9a7467dd8ed94ef317c05328a4054ce445db0f631
bday / block
11899
tx
a4a10..
preasset
doc published by
PrGVS..
Known
notE
notE
:
∀ x0 : ο .
not
x0
⟶
x0
⟶
False
Known
FalseE
FalseE
:
False
⟶
∀ x0 : ο .
x0
Theorem
4f699..
:
∀ x0 : ο .
not
x0
⟶
x0
⟶
∀ x1 : ο .
x1
(proof)
Known
d06ba..
:
not
(
∀ x0 :
(
(
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
)
→
ι → ο
.
∀ x1 :
(
ι → ι
)
→
(
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
)
→
ι → ο
.
∀ x2 :
(
ι →
ι → ι
)
→
(
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
)
→ ο
.
∀ x3 :
(
ι →
ι → ι
)
→
ι →
ι →
ι → ο
.
(
∀ x4 :
ι →
(
ι →
ι → ι
)
→
ι →
ι → ι
.
∀ x5 x6 x7 .
In
(
setsum
(
x4
(
Inj1
0
)
(
λ x8 x9 .
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
x5
0
)
(
setsum
(
x4
(
Inj0
0
)
(
λ x8 x9 .
0
)
(
setsum
0
0
)
0
)
(
setsum
(
Inj1
0
)
0
)
)
)
(
Inj1
(
setsum
x6
0
)
)
⟶
x0
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→ ι
.
λ x9 :
ι →
ι → ι
.
setsum
0
(
setsum
(
x9
(
Inj1
0
)
(
x9
0
0
)
)
x7
)
)
(
x4
(
setsum
(
x4
(
setsum
0
0
)
(
λ x8 x9 .
setsum
0
0
)
x5
(
setsum
0
0
)
)
x7
)
(
λ x8 x9 .
x9
)
(
setsum
(
Inj1
(
x4
0
(
λ x8 x9 .
0
)
0
0
)
)
(
Inj1
(
Inj1
0
)
)
)
0
)
⟶
x3
(
λ x8 x9 .
x9
)
(
setsum
x5
0
)
(
Inj1
0
)
x6
)
⟶
(
∀ x4 .
∀ x5 :
ι →
(
ι → ι
)
→ ι
.
∀ x6 :
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x7 .
In
(
Inj1
0
)
(
setsum
0
0
)
⟶
x3
(
λ x8 x9 .
0
)
(
setsum
0
(
setsum
0
(
Inj1
0
)
)
)
0
(
Inj1
0
)
⟶
x1
(
λ x8 .
setsum
(
setsum
(
Inj0
(
x5
0
(
λ x9 .
0
)
)
)
x8
)
0
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
Inj1
0
)
(
Inj1
(
setsum
(
Inj1
(
setsum
0
0
)
)
(
x5
0
(
λ x8 .
0
)
)
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
∀ x6 :
(
ι → ι
)
→
ι → ι
.
∀ x7 :
(
ι → ι
)
→ ι
.
In
(
Inj1
(
x4
(
setsum
(
x6
(
λ x8 .
0
)
0
)
(
setsum
0
0
)
)
)
)
(
setsum
(
x4
(
setsum
(
Inj0
0
)
0
)
)
(
x4
0
)
)
⟶
x2
(
λ x8 x9 .
x7
(
λ x10 .
0
)
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x9 x10 .
setsum
(
Inj0
0
)
0
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
∀ x5 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x6 :
ι →
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
∀ x7 .
In
(
setsum
0
(
setsum
(
setsum
(
Inj0
0
)
0
)
(
x5
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
λ x9 :
ι → ι
.
λ x10 .
Inj0
0
)
(
λ x8 x9 .
0
)
(
λ x8 .
x5
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 :
ι → ι
.
λ x11 .
0
)
(
λ x9 x10 .
0
)
(
λ x9 .
0
)
)
)
)
)
(
Inj1
(
x5
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
λ x9 :
ι → ι
.
λ x10 .
setsum
x10
0
)
(
λ x8 x9 .
x8
)
(
λ x8 .
Inj1
(
Inj1
0
)
)
)
)
⟶
x2
(
λ x8 x9 .
0
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x9 x10 .
Inj1
(
Inj0
0
)
)
⟶
x1
(
λ x8 .
Inj1
0
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
setsum
(
setsum
(
setsum
(
setsum
0
0
)
(
Inj1
0
)
)
(
setsum
0
x7
)
)
0
)
(
setsum
(
setsum
(
x4
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 :
ι → ι
.
λ x10 .
0
)
(
x6
0
(
λ x8 :
ι → ι
.
0
)
0
0
)
0
)
(
x4
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 :
ι → ι
.
λ x10 .
0
)
(
setsum
0
0
)
(
setsum
0
0
)
)
)
(
setsum
0
(
x6
x7
(
λ x8 :
ι → ι
.
setsum
0
0
)
(
setsum
0
0
)
(
Inj1
0
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
∀ x6 x7 .
x3
(
λ x8 x9 .
x8
)
0
(
Inj1
0
)
(
setsum
0
0
)
⟶
x1
(
λ x8 .
setsum
(
Inj0
x8
)
(
setsum
0
(
setsum
0
(
setsum
0
0
)
)
)
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
0
)
0
)
⟶
(
∀ x4 :
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x5 :
ι → ι
.
∀ x6 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
∀ x7 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
x1
(
λ x8 .
x7
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 :
ι → ι
.
λ x11 .
setsum
(
Inj1
0
)
0
)
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
Inj1
0
)
(
x5
0
)
⟶
x1
(
λ x8 .
setsum
(
x5
0
)
(
Inj0
0
)
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
Inj0
0
)
(
setsum
(
setsum
0
0
)
(
Inj0
(
setsum
0
(
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 :
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x5 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
∀ x6 :
(
(
ι →
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x7 :
ι → ι
.
x0
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→ ι
.
λ x9 :
ι →
ι → ι
.
x9
0
0
)
(
Inj1
(
setsum
0
(
x6
(
λ x8 :
ι →
ι → ι
.
λ x9 .
Inj0
0
)
(
λ x8 :
ι → ι
.
λ x9 .
x9
)
)
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 :
(
ι → ι
)
→
ι → ι
.
∀ x6 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x7 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
In
(
Inj1
(
setsum
(
x7
(
x4
0
)
(
λ x8 :
ι → ι
.
λ x9 .
setsum
0
0
)
)
0
)
)
(
Inj0
0
)
⟶
x0
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→ ι
.
λ x9 :
ι →
ι → ι
.
setsum
0
(
x7
(
x6
(
setsum
0
0
)
(
λ x10 :
ι → ι
.
λ x11 .
Inj1
0
)
(
λ x10 .
setsum
0
0
)
)
(
λ x10 :
ι → ι
.
λ x11 .
setsum
(
x10
0
)
0
)
)
)
(
Inj1
(
setsum
(
x4
(
Inj1
0
)
)
(
Inj0
0
)
)
)
⟶
x3
(
λ x8 x9 .
setsum
(
setsum
(
x6
(
setsum
0
0
)
(
λ x10 :
ι → ι
.
λ x11 .
setsum
0
0
)
(
λ x10 .
x10
)
)
(
Inj1
0
)
)
(
Inj0
0
)
)
0
0
(
x7
0
(
λ x8 :
ι → ι
.
λ x9 .
x9
)
)
)
⟶
False
)
Known
2c194..
:
not
(
∀ x0 :
(
(
(
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→ ι
)
→ ι
)
→
(
ι →
ι →
ι → ι
)
→ ο
.
∀ x1 :
(
(
(
ι →
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι →
(
(
ι → ι
)
→
ι → ι
)
→
ι → ο
.
∀ x2 :
(
ι →
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
)
→
ι →
ι →
(
ι → ι
)
→
ι → ο
.
∀ x3 :
(
ι → ι
)
→
(
(
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ο
.
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 .
∀ x7 :
ι → ι
.
In
(
Inj1
(
setsum
(
setsum
(
Inj0
0
)
(
x5
0
)
)
(
x5
0
)
)
)
(
Inj1
(
Inj0
(
x5
(
x7
0
)
)
)
)
⟶
x3
(
λ x8 .
setsum
(
setsum
(
Inj0
(
Inj1
0
)
)
(
Inj1
(
setsum
0
0
)
)
)
x6
)
(
λ x8 :
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
λ x9 :
(
ι → ι
)
→ ι
.
setsum
0
(
x8
(
λ x10 :
ι → ι
.
λ x11 .
setsum
(
setsum
0
0
)
0
)
(
x7
(
x7
0
)
)
)
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
(
ι →
ι →
ι → ι
)
→
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x7 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
x3
(
λ x8 .
Inj0
(
setsum
(
setsum
(
Inj0
0
)
x8
)
(
x6
(
λ x9 x10 x11 .
x11
)
(
λ x9 .
0
)
(
λ x9 .
0
)
(
Inj0
0
)
)
)
)
(
λ x8 :
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
λ x9 :
(
ι → ι
)
→ ι
.
x8
(
λ x10 :
ι → ι
.
λ x11 .
x10
(
Inj1
0
)
)
(
Inj0
0
)
)
⟶
x1
(
λ x8 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
λ x9 .
x9
)
(
λ x8 .
setsum
(
setsum
0
0
)
0
)
x4
(
λ x8 :
ι → ι
.
λ x9 .
0
)
0
)
⟶
(
∀ x4 :
(
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
∀ x5 :
ι →
ι →
(
ι → ι
)
→ ι
.
∀ x6 :
(
ι → ι
)
→
(
ι → ι
)
→
ι →
ι → ι
.
∀ x7 .
x3
(
λ x8 .
setsum
(
Inj1
0
)
(
Inj1
(
x5
0
(
setsum
0
0
)
(
λ x9 .
x6
(
λ x10 .
0
)
(
λ x10 .
0
)
0
0
)
)
)
)
(
λ x8 :
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
λ x9 :
(
ι → ι
)
→ ι
.
Inj1
(
x9
(
λ x10 .
x8
(
λ x11 :
ι → ι
.
λ x12 .
Inj1
0
)
(
x8
(
λ x11 :
ι → ι
.
λ x12 .
0
)
0
)
)
)
)
⟶
x2
(
λ x8 .
λ x9 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
0
)
0
(
Inj0
(
setsum
(
Inj1
(
x5
0
0
(
λ x8 .
0
)
)
)
(
x4
(
λ x8 :
ι →
ι → ι
.
λ x9 x10 .
Inj0
0
)
)
)
)
(
λ x8 .
0
)
0
)
⟶
(
∀ x4 :
ι →
(
ι → ι
)
→
ι →
ι → ι
.
∀ x5 :
(
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι →
ι →
ι → ι
.
∀ x6 :
ι →
(
ι →
ι → ι
)
→
ι →
ι → ι
.
∀ x7 .
In
x7
(
Inj0
(
x5
(
λ x8 x9 :
ι → ι
.
λ x10 .
Inj1
(
setsum
0
0
)
)
(
Inj0
0
)
(
x6
0
(
λ x8 x9 .
setsum
0
0
)
(
x4
0
(
λ x8 .
0
)
0
0
)
0
)
x7
)
)
⟶
x2
(
λ x8 .
λ x9 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
setsum
(
setsum
x8
(
x9
(
λ x10 x11 .
Inj1
0
)
(
λ x10 .
setsum
0
0
)
)
)
(
setsum
x8
(
Inj0
(
x9
(
λ x10 x11 .
0
)
(
λ x10 .
0
)
)
)
)
)
0
0
(
setsum
(
x5
(
λ x8 x9 :
ι → ι
.
λ x10 .
Inj0
(
x9
0
)
)
(
x6
(
Inj1
0
)
(
λ x8 x9 .
setsum
0
0
)
(
setsum
0
0
)
(
Inj1
0
)
)
(
Inj1
(
setsum
0
0
)
)
(
setsum
(
Inj1
0
)
0
)
)
)
0
⟶
x0
(
λ x8 :
(
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
setsum
0
(
Inj0
(
setsum
(
Inj0
0
)
(
setsum
0
0
)
)
)
)
(
λ x8 x9 x10 .
x7
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
∀ x6 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι → ι
.
∀ x7 :
ι → ι
.
In
(
Inj0
(
setsum
(
Inj1
(
x7
0
)
)
0
)
)
(
setsum
(
setsum
0
(
setsum
(
Inj0
0
)
(
x5
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
0
)
)
)
)
(
Inj1
(
Inj1
0
)
)
)
⟶
x0
(
λ x8 :
(
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
Inj1
(
Inj0
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
)
(
λ x8 x9 x10 .
x8
)
⟶
x1
(
λ x8 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
x8
(
λ x9 .
λ x10 :
ι → ι
.
0
)
(
x7
0
)
)
(
λ x8 .
0
)
0
(
λ x8 :
ι → ι
.
λ x9 .
x7
(
Inj0
(
Inj1
(
x6
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
0
)
0
)
)
)
)
(
setsum
(
Inj1
0
)
(
setsum
(
Inj1
(
Inj0
0
)
)
(
setsum
(
x7
0
)
(
Inj0
0
)
)
)
)
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
ι →
ι →
ι → ι
.
In
x5
(
setsum
x6
(
setsum
0
0
)
)
⟶
x1
(
λ x8 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
λ x9 .
x9
)
(
λ x8 .
Inj1
(
Inj1
x8
)
)
0
(
λ x8 :
ι → ι
.
λ x9 .
Inj0
(
x8
x9
)
)
x5
⟶
x3
(
λ x8 .
Inj1
(
setsum
x6
(
setsum
0
x8
)
)
)
(
λ x8 :
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
λ x9 :
(
ι → ι
)
→ ι
.
Inj0
(
setsum
(
Inj1
(
x9
(
λ x10 .
0
)
)
)
(
x7
(
x7
0
0
0
)
(
Inj1
0
)
(
Inj1
0
)
)
)
)
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
ι → ι
.
x0
(
λ x8 :
(
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
setsum
x6
(
Inj1
(
setsum
(
Inj1
0
)
(
setsum
0
0
)
)
)
)
(
λ x8 x9 x10 .
Inj1
(
Inj0
0
)
)
⟶
x0
(
λ x8 :
(
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
0
)
(
λ x8 x9 x10 .
Inj1
(
Inj1
(
Inj1
(
Inj1
0
)
)
)
)
)
⟶
(
∀ x4 :
ι →
ι →
(
ι → ι
)
→ ι
.
∀ x5 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
∀ x6 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
∀ x7 .
x0
(
λ x8 :
(
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
x6
0
0
(
λ x9 .
0
)
0
)
(
λ x8 x9 x10 .
0
)
⟶
x0
(
λ x8 :
(
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
x6
(
x8
(
λ x9 :
ι →
ι → ι
.
λ x10 x11 .
x9
(
x8
(
λ x12 :
ι →
ι → ι
.
λ x13 x14 .
0
)
)
(
setsum
0
0
)
)
)
(
setsum
0
(
setsum
(
Inj0
0
)
0
)
)
(
λ x9 .
setsum
0
(
setsum
(
x6
0
0
(
λ x10 .
0
)
0
)
0
)
)
(
setsum
(
Inj1
(
setsum
0
0
)
)
(
x8
(
λ x9 :
ι →
ι → ι
.
λ x10 x11 .
0
)
)
)
)
(
λ x8 x9 x10 .
x10
)
)
⟶
False
)
Known
95285..
:
not
(
∀ x0 :
(
(
ι →
ι →
ι → ι
)
→
ι →
ι → ι
)
→
ι → ο
.
∀ x1 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ο
.
∀ x2 :
(
ι → ι
)
→
ι → ο
.
∀ x3 :
(
ι →
ι →
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
)
→ ο
.
(
∀ x4 :
ι →
ι → ι
.
∀ x5 .
∀ x6 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
∀ x7 :
(
ι →
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
In
(
setsum
0
(
x7
(
λ x8 .
λ x9 :
ι → ι
.
x7
(
λ x10 .
λ x11 :
ι → ι
.
0
)
(
λ x10 .
setsum
0
0
)
0
)
(
λ x8 .
0
)
(
Inj1
(
x6
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
0
)
)
)
)
)
(
setsum
(
x7
(
λ x8 .
λ x9 :
ι → ι
.
x7
(
λ x10 .
λ x11 :
ι → ι
.
0
)
(
λ x10 .
Inj1
0
)
(
x6
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
0
)
)
)
(
λ x8 .
Inj1
(
setsum
0
0
)
)
0
)
(
setsum
(
x6
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
0
)
)
(
setsum
(
setsum
0
0
)
(
Inj1
0
)
)
)
)
⟶
x3
(
λ x8 x9 x10 x11 x12 .
Inj0
0
)
(
λ x8 :
ι → ι
.
λ x9 :
ι →
ι → ι
.
x8
(
x6
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
0
)
)
)
)
⟶
(
∀ x4 :
ι →
(
ι →
ι → ι
)
→
ι →
ι → ι
.
∀ x5 :
(
ι →
ι →
ι → ι
)
→
ι →
ι → ι
.
∀ x6 .
∀ x7 :
(
ι → ι
)
→ ι
.
In
(
Inj1
(
setsum
(
x5
(
λ x8 x9 x10 .
Inj0
0
)
(
setsum
0
0
)
(
setsum
0
0
)
)
(
setsum
x6
(
x7
(
λ x8 .
0
)
)
)
)
)
x6
⟶
x3
(
λ x8 x9 x10 x11 x12 .
Inj1
(
setsum
(
Inj1
0
)
x12
)
)
(
λ x8 :
ι → ι
.
λ x9 :
ι →
ι → ι
.
Inj1
(
Inj1
(
Inj0
(
Inj1
0
)
)
)
)
⟶
x3
(
λ x8 x9 x10 x11 x12 .
Inj1
(
setsum
0
(
setsum
(
Inj0
0
)
0
)
)
)
(
λ x8 :
ι → ι
.
λ x9 :
ι →
ι → ι
.
Inj0
(
Inj0
(
x9
(
x7
(
λ x10 .
0
)
)
(
x7
(
λ x10 .
0
)
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
(
ι → ι
)
→ ι
.
∀ x6 x7 .
In
(
Inj0
x7
)
(
setsum
0
0
)
⟶
x2
(
λ x8 .
0
)
x6
⟶
x2
(
λ x8 .
0
)
(
Inj1
0
)
)
⟶
(
∀ x4 x5 x6 x7 .
x2
(
λ x8 .
x6
)
x4
⟶
In
x5
(
Inj1
0
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→
ι → ι
.
∀ x5 :
(
(
ι →
ι → ι
)
→ ι
)
→ ι
.
∀ x6 .
∀ x7 :
ι → ι
.
In
(
x5
(
λ x8 :
ι →
ι → ι
.
0
)
)
(
x5
(
λ x8 :
ι →
ι → ι
.
Inj0
(
x8
(
Inj1
0
)
(
setsum
0
0
)
)
)
)
⟶
x1
(
λ x8 :
ι → ι
.
Inj0
0
)
(
λ x8 .
0
)
(
x5
(
λ x8 :
ι →
ι → ι
.
0
)
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
(
ι → ι
)
→
ι → ι
.
∀ x7 .
x1
(
λ x8 :
ι → ι
.
x6
(
λ x9 .
x7
)
(
Inj1
(
Inj0
(
Inj1
0
)
)
)
)
(
λ x8 .
setsum
(
x6
(
λ x9 .
setsum
x9
0
)
(
Inj1
(
Inj1
0
)
)
)
0
)
(
setsum
0
(
Inj1
0
)
)
⟶
x0
(
λ x8 :
ι →
ι →
ι → ι
.
λ x9 x10 .
setsum
x7
(
setsum
x10
(
x8
(
setsum
0
0
)
0
(
setsum
0
0
)
)
)
)
0
)
⟶
(
∀ x4 x5 .
∀ x6 :
ι → ι
.
∀ x7 .
x0
(
λ x8 :
ι →
ι →
ι → ι
.
λ x9 x10 .
0
)
0
⟶
x0
(
λ x8 :
ι →
ι →
ι → ι
.
λ x9 x10 .
0
)
(
Inj1
x7
)
)
⟶
(
∀ x4 x5 x6 x7 .
x0
(
λ x8 :
ι →
ι →
ι → ι
.
λ x9 x10 .
x10
)
(
Inj0
0
)
⟶
x3
(
λ x8 x9 x10 x11 x12 .
Inj1
0
)
(
λ x8 :
ι → ι
.
λ x9 :
ι →
ι → ι
.
0
)
)
⟶
False
)
Known
acf72..
:
not
(
∀ x0 :
(
(
(
ι → ι
)
→
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι →
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ο
.
∀ x1 :
(
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ο
.
∀ x2 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ο
.
∀ x3 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
(
ι →
ι → ι
)
→ ι
)
→
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι → ο
.
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x7 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
In
(
Inj1
(
x5
0
)
)
(
Inj0
(
Inj1
(
Inj1
(
setsum
0
0
)
)
)
)
⟶
x2
(
λ x8 .
x7
(
λ x9 .
setsum
(
setsum
(
setsum
0
0
)
0
)
(
x6
(
λ x10 .
λ x11 :
ι → ι
.
λ x12 .
Inj1
0
)
)
)
(
λ x9 :
ι → ι
.
λ x10 .
setsum
0
(
x7
(
λ x11 .
Inj0
0
)
(
λ x11 :
ι → ι
.
λ x12 .
0
)
)
)
)
(
λ x8 x9 .
0
)
⟶
x3
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 .
setsum
(
x8
(
λ x10 .
setsum
(
setsum
0
0
)
(
Inj0
0
)
)
)
0
)
(
λ x8 :
ι →
ι → ι
.
Inj0
0
)
(
λ x8 :
(
ι → ι
)
→ ι
.
0
)
(
Inj1
0
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 x6 .
∀ x7 :
ι → ι
.
x3
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 .
setsum
(
x7
(
setsum
x9
(
Inj1
0
)
)
)
(
Inj0
(
setsum
0
(
Inj1
0
)
)
)
)
(
λ x8 :
ι →
ι → ι
.
0
)
(
λ x8 :
(
ι → ι
)
→ ι
.
setsum
x6
(
setsum
(
x8
(
λ x9 .
Inj0
0
)
)
(
x7
0
)
)
)
(
setsum
(
setsum
(
x7
0
)
x5
)
(
Inj1
(
setsum
(
Inj1
0
)
(
setsum
0
0
)
)
)
)
⟶
In
(
Inj0
0
)
(
Inj1
0
)
)
⟶
(
∀ x4 x5 x6 x7 .
In
(
Inj1
x7
)
(
Inj0
(
Inj0
x5
)
)
⟶
x3
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 .
Inj0
(
setsum
(
setsum
(
Inj0
0
)
0
)
(
setsum
0
(
x8
(
λ x10 .
0
)
)
)
)
)
(
λ x8 :
ι →
ι → ι
.
0
)
(
λ x8 :
(
ι → ι
)
→ ι
.
x6
)
(
Inj0
0
)
⟶
x2
(
λ x8 .
Inj0
x6
)
(
λ x8 x9 .
setsum
(
setsum
0
0
)
x6
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
∀ x5 x6 .
∀ x7 :
ι → ι
.
x2
(
λ x8 .
0
)
(
λ x8 x9 .
0
)
⟶
In
(
Inj0
x6
)
(
setsum
x6
(
Inj1
(
Inj0
(
Inj0
0
)
)
)
)
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
ι → ι
.
In
(
Inj0
0
)
(
Inj1
(
setsum
x6
0
)
)
⟶
x2
(
λ x8 .
Inj0
0
)
(
λ x8 x9 .
setsum
(
x7
(
setsum
0
0
)
)
0
)
⟶
x1
(
λ x8 x9 .
0
)
(
λ x8 :
ι → ι
.
x6
)
)
⟶
(
∀ x4 x5 x6 x7 .
x1
(
λ x8 x9 .
setsum
(
setsum
0
(
setsum
(
Inj1
0
)
x7
)
)
(
Inj1
(
setsum
x6
x6
)
)
)
(
λ x8 :
ι → ι
.
0
)
⟶
x1
(
λ x8 x9 .
x6
)
(
λ x8 :
ι → ι
.
x7
)
)
⟶
(
∀ x4 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
∀ x5 :
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
∀ x6 .
∀ x7 :
ι →
ι → ι
.
x2
(
λ x8 .
0
)
(
λ x8 x9 .
Inj1
0
)
⟶
x0
(
λ x8 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
(
ι → ι
)
→
ι → ι
.
0
)
(
x7
(
setsum
(
Inj0
(
setsum
0
0
)
)
(
setsum
(
setsum
0
0
)
(
Inj0
0
)
)
)
(
Inj1
(
setsum
0
(
setsum
0
0
)
)
)
)
(
setsum
0
(
setsum
(
x4
(
setsum
0
0
)
0
(
λ x8 .
setsum
0
0
)
(
setsum
0
0
)
)
(
setsum
(
x7
0
0
)
(
Inj1
0
)
)
)
)
(
λ x8 :
ι → ι
.
λ x9 .
setsum
x9
(
Inj0
x9
)
)
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
ι → ι
.
x0
(
λ x8 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
(
ι → ι
)
→
ι → ι
.
0
)
x6
x5
(
λ x8 :
ι → ι
.
λ x9 .
setsum
(
Inj1
(
setsum
(
Inj1
0
)
x9
)
)
(
Inj0
x9
)
)
⟶
x2
(
λ x8 .
Inj0
(
x7
0
)
)
(
λ x8 x9 .
x6
)
)
⟶
False
)
Known
748af..
:
not
(
∀ x0 :
(
ι → ι
)
→
ι → ο
.
∀ x1 :
(
ι →
(
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
)
→
(
(
ι →
(
ι → ι
)
→ ι
)
→ ι
)
→ ο
.
∀ x2 :
(
ι → ι
)
→
ι →
ι →
ι → ο
.
∀ x3 :
(
(
(
ι →
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι →
ι → ι
)
→
ι → ι
)
→
ι → ο
.
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 :
(
ι → ι
)
→ ι
.
∀ x7 :
ι → ι
.
In
(
Inj1
(
setsum
(
Inj0
(
setsum
0
0
)
)
x4
)
)
(
Inj1
(
x7
(
setsum
0
(
setsum
0
0
)
)
)
)
⟶
x1
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
λ x12 .
x12
)
(
λ x8 :
ι →
(
ι → ι
)
→ ι
.
x5
0
)
⟶
x3
(
λ x8 :
(
ι →
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x9 .
λ x10 :
ι →
ι → ι
.
λ x11 .
Inj1
(
Inj1
(
setsum
(
setsum
0
0
)
(
Inj0
0
)
)
)
)
(
x5
(
setsum
(
Inj1
(
Inj1
0
)
)
0
)
)
)
⟶
(
∀ x4 :
ι →
(
ι →
ι → ι
)
→
ι → ι
.
∀ x5 x6 x7 .
x3
(
λ x8 :
(
ι →
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x9 .
λ x10 :
ι →
ι → ι
.
λ x11 .
setsum
(
x8
(
λ x12 x13 x14 .
Inj1
(
Inj1
0
)
)
(
λ x12 .
Inj0
0
)
(
x10
(
x10
0
0
)
0
)
)
(
Inj1
0
)
)
x7
⟶
x3
(
λ x8 :
(
ι →
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x9 .
λ x10 :
ι →
ι → ι
.
λ x11 .
0
)
x7
)
⟶
(
∀ x4 .
∀ x5 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x6 :
ι → ι
.
∀ x7 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
x2
(
λ x8 .
x7
(
λ x9 :
ι → ι
.
0
)
(
Inj0
(
setsum
0
0
)
)
)
0
(
Inj1
0
)
(
Inj0
(
setsum
(
x5
(
Inj1
0
)
(
λ x8 :
ι → ι
.
x7
(
λ x9 :
ι → ι
.
0
)
0
)
)
(
x6
x4
)
)
)
⟶
x2
(
λ x8 .
Inj0
0
)
(
setsum
x4
(
Inj0
(
x5
0
(
λ x8 :
ι → ι
.
setsum
0
0
)
)
)
)
x4
0
)
⟶
(
∀ x4 x5 x6 x7 .
x2
(
λ x8 .
0
)
(
Inj0
(
Inj1
x4
)
)
(
Inj0
(
setsum
(
Inj0
0
)
0
)
)
(
setsum
(
setsum
x4
0
)
0
)
⟶
In
x7
(
Inj1
0
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
∀ x6 .
∀ x7 :
(
ι →
ι → ι
)
→
ι →
ι → ι
.
x3
(
λ x8 :
(
ι →
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x9 .
λ x10 :
ι →
ι → ι
.
λ x11 .
setsum
0
(
Inj0
(
Inj1
(
x10
0
0
)
)
)
)
(
Inj1
0
)
⟶
x1
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
λ x12 .
x12
)
(
λ x8 :
ι →
(
ι → ι
)
→ ι
.
x5
0
(
setsum
(
Inj0
(
setsum
0
0
)
)
0
)
(
λ x9 .
x6
)
(
x8
(
setsum
(
Inj1
0
)
0
)
(
λ x9 .
0
)
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 .
∀ x6 :
(
ι → ι
)
→
ι →
ι → ι
.
∀ x7 .
x1
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
λ x12 .
0
)
(
λ x8 :
ι →
(
ι → ι
)
→ ι
.
0
)
⟶
False
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 :
(
ι →
ι →
ι → ι
)
→ ι
.
∀ x7 .
In
(
Inj1
(
Inj0
(
setsum
0
(
x6
(
λ x8 x9 x10 .
0
)
)
)
)
)
(
Inj0
(
setsum
x4
0
)
)
⟶
x3
(
λ x8 :
(
ι →
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x9 .
λ x10 :
ι →
ι → ι
.
λ x11 .
0
)
x7
⟶
x0
(
λ x8 .
Inj0
(
Inj0
(
setsum
(
x5
0
)
(
Inj1
0
)
)
)
)
(
Inj1
0
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x7 .
In
(
Inj1
0
)
x4
⟶
x0
(
λ x8 .
setsum
0
(
Inj0
(
x6
(
λ x9 :
ι → ι
.
λ x10 .
0
)
)
)
)
(
setsum
x7
x7
)
⟶
x3
(
λ x8 :
(
ι →
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x9 .
λ x10 :
ι →
ι → ι
.
λ x11 .
0
)
(
Inj1
(
Inj1
x5
)
)
)
⟶
False
)
Known
56955..
:
not
(
∀ x0 :
(
ι →
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι →
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ο
.
∀ x1 :
(
(
(
(
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→
ι → ο
.
∀ x2 :
(
ι →
(
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
)
→ ι
)
→
ι → ο
.
∀ x3 :
(
ι → ι
)
→
(
(
ι →
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→ ι
)
→ ο
.
(
∀ x4 x5 .
∀ x6 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
.
∀ x7 :
ι →
ι → ι
.
In
(
Inj1
(
Inj1
x4
)
)
x4
⟶
x0
(
λ x8 .
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
0
)
(
setsum
(
x7
0
x4
)
(
Inj0
(
setsum
(
Inj0
0
)
0
)
)
)
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
setsum
(
Inj0
(
setsum
x5
x5
)
)
(
Inj1
0
)
)
⟶
x3
(
λ x8 .
x6
(
λ x9 :
(
ι → ι
)
→ ι
.
setsum
(
Inj1
(
setsum
0
0
)
)
(
x7
(
Inj1
0
)
0
)
)
)
(
λ x8 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x9 .
λ x10 :
ι → ι
.
0
)
)
⟶
(
∀ x4 .
∀ x5 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→ ι
.
∀ x6 x7 .
x3
(
λ x8 .
0
)
(
λ x8 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x9 .
λ x10 :
ι → ι
.
setsum
(
Inj1
(
setsum
x7
(
Inj1
0
)
)
)
0
)
⟶
False
)
⟶
(
∀ x4 :
ι →
ι → ι
.
∀ x5 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
.
∀ x6 x7 .
x1
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→ ι
.
λ x9 x10 .
0
)
(
setsum
(
setsum
(
x5
(
λ x8 :
(
ι → ι
)
→ ι
.
setsum
0
0
)
)
(
Inj0
(
Inj1
0
)
)
)
(
x4
(
Inj1
(
setsum
0
0
)
)
(
Inj0
0
)
)
)
⟶
x2
(
λ x8 .
λ x9 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
Inj0
x8
)
(
Inj1
(
setsum
x7
(
setsum
0
(
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
(
ι →
ι → ι
)
→ ι
.
∀ x6 .
∀ x7 :
(
(
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
x2
(
λ x8 .
λ x9 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
Inj0
(
setsum
(
Inj1
(
setsum
0
0
)
)
x6
)
)
(
Inj0
(
Inj0
(
Inj1
(
Inj1
0
)
)
)
)
⟶
x1
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→ ι
.
λ x9 x10 .
0
)
0
)
⟶
(
∀ x4 .
∀ x5 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x6 x7 :
ι → ι
.
In
(
setsum
0
(
setsum
(
setsum
(
x5
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
0
)
)
(
setsum
0
0
)
)
(
Inj1
(
Inj0
0
)
)
)
)
(
Inj0
(
setsum
(
Inj0
(
Inj0
0
)
)
0
)
)
⟶
x3
(
λ x8 .
setsum
0
(
Inj0
(
Inj1
(
Inj0
0
)
)
)
)
(
λ x8 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x9 .
λ x10 :
ι → ι
.
0
)
⟶
x1
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→ ι
.
λ x9 x10 .
setsum
(
Inj1
0
)
(
Inj1
0
)
)
(
setsum
0
(
setsum
0
0
)
)
)
⟶
(
∀ x4 :
(
ι →
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
∀ x5 :
ι →
(
ι →
ι → ι
)
→ ι
.
∀ x6 .
∀ x7 :
ι → ι
.
x1
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→ ι
.
λ x9 x10 .
0
)
(
setsum
(
x7
(
x5
0
(
λ x8 x9 .
0
)
)
)
(
setsum
x6
x6
)
)
⟶
In
(
Inj1
(
setsum
(
Inj0
(
setsum
0
0
)
)
(
setsum
(
Inj1
0
)
(
setsum
0
0
)
)
)
)
(
x4
(
λ x8 x9 .
setsum
(
setsum
x6
0
)
(
Inj0
(
x7
0
)
)
)
(
setsum
0
0
)
(
λ x8 .
0
)
(
setsum
(
x7
(
setsum
0
0
)
)
(
Inj1
(
Inj0
0
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
ι → ι
.
∀ x6 :
ι → ι
.
∀ x7 .
x3
(
λ x8 .
x7
)
(
λ x8 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x9 .
λ x10 :
ι → ι
.
setsum
0
(
Inj0
(
setsum
(
x8
0
(
λ x11 .
0
)
0
)
0
)
)
)
⟶
x0
(
λ x8 .
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
x8
)
(
setsum
(
setsum
(
Inj0
0
)
x4
)
0
)
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
Inj1
(
setsum
0
(
x6
(
x5
0
0
)
)
)
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
(
(
ι → ι
)
→
ι →
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x7 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
x0
(
λ x8 .
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
Inj0
0
)
(
setsum
0
(
x7
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
setsum
(
x7
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
0
)
)
(
Inj1
0
)
)
)
)
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
x5
)
⟶
False
)
⟶
False
)
Known
16fbe..
:
not
(
∀ x0 :
(
ι → ι
)
→
ι →
ι → ο
.
∀ x1 :
(
(
ι → ι
)
→ ι
)
→
(
(
ι →
ι →
ι → ι
)
→ ι
)
→
(
ι →
ι →
ι → ι
)
→ ο
.
∀ x2 :
(
ι → ι
)
→
(
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
)
→
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ο
.
∀ x3 :
(
(
ι →
(
ι → ι
)
→ ι
)
→
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
)
→
(
(
ι →
ι →
ι → ι
)
→ ι
)
→
(
ι →
ι →
ι → ι
)
→
ι → ο
.
(
∀ x4 :
ι →
(
ι →
ι → ι
)
→ ι
.
∀ x5 .
∀ x6 :
ι →
ι → ι
.
∀ x7 .
x0
(
λ x8 .
0
)
(
setsum
0
(
Inj1
(
setsum
x7
(
setsum
0
0
)
)
)
)
(
setsum
(
x4
(
x6
(
Inj0
0
)
(
setsum
0
0
)
)
(
λ x8 x9 .
x9
)
)
(
setsum
0
x7
)
)
⟶
x3
(
λ x8 :
ι →
(
ι → ι
)
→ ι
.
λ x9 :
(
(
ι → ι
)
→ ι
)
→ ι
.
0
)
(
λ x8 :
ι →
ι →
ι → ι
.
0
)
(
λ x8 x9 x10 .
setsum
(
Inj1
(
Inj0
(
Inj1
0
)
)
)
(
Inj0
0
)
)
(
setsum
(
Inj0
(
setsum
(
Inj1
0
)
(
Inj1
0
)
)
)
0
)
)
⟶
(
∀ x4 :
(
(
ι →
ι → ι
)
→ ι
)
→ ι
.
∀ x5 :
ι → ι
.
∀ x6 x7 .
In
x7
(
Inj1
(
Inj1
(
Inj0
x6
)
)
)
⟶
x3
(
λ x8 :
ι →
(
ι → ι
)
→ ι
.
λ x9 :
(
(
ι → ι
)
→ ι
)
→ ι
.
0
)
(
λ x8 :
ι →
ι →
ι → ι
.
setsum
(
Inj1
(
Inj1
(
setsum
0
0
)
)
)
0
)
(
λ x8 x9 x10 .
setsum
0
(
Inj0
(
Inj1
(
Inj0
0
)
)
)
)
0
⟶
x3
(
λ x8 :
ι →
(
ι → ι
)
→ ι
.
λ x9 :
(
(
ι → ι
)
→ ι
)
→ ι
.
Inj1
(
setsum
(
Inj1
(
x8
0
(
λ x10 .
0
)
)
)
0
)
)
(
λ x8 :
ι →
ι →
ι → ι
.
setsum
(
Inj1
0
)
(
setsum
0
0
)
)
(
λ x8 x9 x10 .
x9
)
(
x4
(
λ x8 :
ι →
ι → ι
.
setsum
x7
(
setsum
(
Inj0
0
)
(
x8
0
0
)
)
)
)
)
⟶
(
∀ x4 x5 x6 x7 .
x2
(
λ x8 .
setsum
(
Inj1
0
)
(
Inj1
0
)
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 x11 .
x9
(
λ x12 .
Inj0
(
Inj0
(
setsum
0
0
)
)
)
0
)
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 x10 .
Inj0
(
Inj1
0
)
)
(
Inj1
(
Inj0
(
setsum
0
0
)
)
)
(
λ x8 .
setsum
(
Inj1
0
)
(
setsum
0
(
setsum
(
Inj0
0
)
x5
)
)
)
0
⟶
x2
(
λ x8 .
setsum
0
0
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 x11 .
setsum
(
setsum
x10
0
)
(
setsum
(
Inj1
(
Inj1
0
)
)
(
setsum
(
x8
(
λ x12 :
ι → ι
.
0
)
)
x10
)
)
)
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 x10 .
Inj1
(
x8
(
λ x11 .
setsum
(
setsum
0
0
)
(
Inj0
0
)
)
)
)
(
setsum
(
Inj1
(
Inj0
x6
)
)
(
Inj1
(
setsum
0
(
Inj1
0
)
)
)
)
(
λ x8 .
Inj1
(
Inj0
(
setsum
(
Inj0
0
)
(
Inj0
0
)
)
)
)
(
setsum
x7
(
Inj1
0
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 x6 x7 .
In
x7
(
Inj0
0
)
⟶
x2
(
λ x8 .
0
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 x11 .
x10
)
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 x10 .
0
)
(
Inj1
(
setsum
x7
(
setsum
(
Inj0
0
)
0
)
)
)
(
λ x8 .
x8
)
(
setsum
(
Inj1
(
x4
(
Inj0
0
)
)
)
(
Inj1
x7
)
)
⟶
x2
Inj0
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 x11 .
x8
(
λ x12 :
ι → ι
.
0
)
)
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 x10 .
setsum
x7
0
)
(
setsum
(
setsum
0
0
)
0
)
(
λ x8 .
Inj0
(
Inj0
x5
)
)
0
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 .
∀ x6 :
ι → ι
.
∀ x7 :
(
ι →
ι →
ι → ι
)
→ ι
.
In
(
setsum
(
Inj0
(
Inj0
(
Inj1
0
)
)
)
(
setsum
0
x5
)
)
(
x4
(
setsum
(
setsum
x5
(
setsum
0
0
)
)
(
Inj1
x5
)
)
)
⟶
x2
(
λ x8 .
setsum
(
x7
(
λ x9 x10 x11 .
0
)
)
x5
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 x11 .
0
)
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 x10 .
x8
(
λ x11 .
setsum
x10
0
)
)
(
setsum
0
(
setsum
(
Inj1
0
)
(
Inj0
x5
)
)
)
(
λ x8 .
x7
(
λ x9 x10 x11 .
setsum
(
setsum
(
setsum
0
0
)
(
Inj1
0
)
)
(
Inj0
(
Inj1
0
)
)
)
)
(
Inj1
(
Inj1
0
)
)
⟶
x1
(
λ x8 :
ι → ι
.
0
)
(
λ x8 :
ι →
ι →
ι → ι
.
Inj1
0
)
(
λ x8 x9 x10 .
x10
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→ ι
.
∀ x5 .
∀ x6 :
(
ι →
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x7 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
x1
(
λ x8 :
ι → ι
.
Inj1
(
setsum
(
x7
(
λ x9 .
λ x10 :
ι → ι
.
0
)
)
(
setsum
0
0
)
)
)
(
λ x8 :
ι →
ι →
ι → ι
.
x6
(
λ x9 x10 .
x9
)
(
λ x9 :
ι → ι
.
λ x10 .
x8
0
(
x8
(
setsum
0
0
)
(
Inj1
0
)
(
Inj0
0
)
)
0
)
(
λ x9 .
Inj1
(
Inj0
0
)
)
)
(
λ x8 x9 x10 .
x9
)
⟶
x0
(
λ x8 .
setsum
0
(
Inj1
(
setsum
0
(
x7
(
λ x9 .
λ x10 :
ι → ι
.
0
)
)
)
)
)
0
(
setsum
(
setsum
(
setsum
(
x6
(
λ x8 x9 .
0
)
(
λ x8 :
ι → ι
.
λ x9 .
0
)
(
λ x8 .
0
)
)
0
)
(
setsum
0
(
setsum
0
0
)
)
)
(
x6
(
λ x8 x9 .
x7
(
λ x10 .
λ x11 :
ι → ι
.
Inj1
0
)
)
(
λ x8 :
ι → ι
.
λ x9 .
x8
(
setsum
0
0
)
)
(
λ x8 .
setsum
0
(
x7
(
λ x9 .
λ x10 :
ι → ι
.
0
)
)
)
)
)
)
⟶
(
∀ x4 :
(
ι →
ι →
ι → ι
)
→ ι
.
∀ x5 :
ι →
ι → ι
.
∀ x6 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
∀ x7 .
x0
(
λ x8 .
0
)
(
setsum
(
Inj1
(
x6
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
0
)
(
Inj0
0
)
0
)
)
x7
)
(
setsum
(
x4
(
λ x8 x9 x10 .
Inj0
(
setsum
0
0
)
)
)
0
)
⟶
x0
(
λ x8 .
setsum
(
setsum
(
Inj1
(
Inj0
0
)
)
(
setsum
(
Inj0
0
)
0
)
)
(
x5
0
(
Inj0
(
setsum
0
0
)
)
)
)
(
Inj1
(
Inj1
(
x5
(
x6
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
0
)
0
0
)
(
Inj0
0
)
)
)
)
(
Inj1
(
Inj1
(
Inj1
0
)
)
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
ι →
(
ι →
ι → ι
)
→ ι
.
∀ x7 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
x0
(
λ x8 .
x5
)
0
(
setsum
0
x5
)
⟶
False
)
⟶
False
)
Known
5be0e..
:
not
(
∀ x0 :
(
(
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι →
ι →
ι → ι
)
→
(
(
ι →
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→ ι
)
→
ι → ο
.
∀ x1 :
(
(
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→ ι
)
→ ι
)
→
(
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ο
.
∀ x2 :
(
(
ι →
ι →
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→
ι → ο
.
∀ x3 :
(
(
ι → ι
)
→
ι →
(
ι →
ι → ι
)
→ ι
)
→
(
ι →
ι →
ι →
ι → ι
)
→
(
(
ι →
ι → ι
)
→
ι → ι
)
→ ο
.
(
∀ x4 :
ι → ι
.
∀ x5 x6 .
∀ x7 :
ι →
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
In
(
x7
(
setsum
0
0
)
(
λ x8 .
0
)
(
setsum
(
setsum
(
setsum
0
0
)
(
Inj0
0
)
)
)
)
(
x7
(
setsum
(
setsum
(
x4
0
)
(
setsum
0
0
)
)
(
x4
(
Inj0
0
)
)
)
(
λ x8 .
setsum
0
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
(
λ x8 .
0
)
)
⟶
x0
(
λ x8 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x9 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 x11 x12 .
setsum
(
x9
(
λ x13 :
ι → ι
.
x13
(
x13
0
)
)
)
(
setsum
0
(
x9
(
λ x13 :
ι → ι
.
0
)
)
)
)
(
λ x8 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x9 .
λ x10 :
ι → ι
.
x7
0
(
λ x11 .
setsum
(
setsum
(
setsum
0
0
)
(
Inj0
0
)
)
(
Inj1
(
setsum
0
0
)
)
)
(
λ x11 .
setsum
(
x8
(
setsum
0
0
)
(
λ x12 .
0
)
(
x8
0
(
λ x12 .
0
)
0
)
)
(
Inj0
0
)
)
)
(
Inj1
(
Inj0
(
setsum
(
Inj1
0
)
0
)
)
)
⟶
x3
(
λ x8 :
ι → ι
.
λ x9 .
λ x10 :
ι →
ι → ι
.
Inj1
(
setsum
(
setsum
(
setsum
0
0
)
x9
)
0
)
)
(
λ x8 x9 x10 x11 .
x8
)
(
λ x8 :
ι →
ι → ι
.
λ x9 .
0
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
ι → ι
.
∀ x7 :
ι →
(
ι → ι
)
→ ι
.
x3
(
λ x8 :
ι → ι
.
λ x9 .
λ x10 :
ι →
ι → ι
.
Inj1
(
Inj1
(
setsum
(
setsum
0
0
)
(
x10
0
0
)
)
)
)
(
λ x8 x9 x10 x11 .
setsum
x9
(
setsum
(
setsum
x11
(
Inj0
0
)
)
x10
)
)
(
λ x8 :
ι →
ι → ι
.
λ x9 .
x8
0
(
Inj0
0
)
)
⟶
x2
(
λ x8 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
λ x9 .
x7
x9
(
λ x10 .
Inj0
(
Inj1
0
)
)
)
0
)
⟶
(
∀ x4 .
∀ x5 :
(
ι → ι
)
→ ι
.
∀ x6 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
∀ x7 :
ι →
(
ι →
ι → ι
)
→ ι
.
x0
(
λ x8 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x9 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 x11 x12 .
x12
)
(
λ x8 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x9 .
λ x10 :
ι → ι
.
x9
)
(
Inj1
(
Inj0
0
)
)
⟶
x2
(
λ x8 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
λ x9 .
0
)
(
Inj1
0
)
)
⟶
(
∀ x4 x5 x6 x7 .
x2
(
λ x8 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
λ x9 .
x7
)
(
setsum
(
setsum
(
setsum
(
Inj0
0
)
(
Inj0
0
)
)
0
)
0
)
⟶
In
(
Inj0
0
)
x7
)
⟶
(
∀ x4 x5 .
∀ x6 :
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
∀ x7 .
In
(
setsum
0
(
setsum
0
0
)
)
x5
⟶
x2
(
λ x8 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
λ x9 .
setsum
(
Inj1
0
)
(
setsum
0
(
x6
(
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 :
ι → ι
.
x11
0
)
0
(
λ x10 .
x7
)
(
Inj0
0
)
)
)
)
0
⟶
x1
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→ ι
.
x6
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
setsum
(
x9
(
λ x11 .
Inj0
0
)
)
0
)
x5
(
λ x9 .
setsum
x7
0
)
x5
)
(
λ x8 :
ι →
(
ι → ι
)
→
ι → ι
.
Inj1
0
)
)
⟶
(
∀ x4 .
∀ x5 :
(
ι →
ι → ι
)
→
ι → ι
.
∀ x6 :
(
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
∀ x7 :
ι →
(
ι →
ι → ι
)
→ ι
.
x1
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→ ι
.
Inj0
0
)
(
λ x8 :
ι →
(
ι → ι
)
→
ι → ι
.
0
)
⟶
x1
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→ ι
.
0
)
(
λ x8 :
ι →
(
ι → ι
)
→
ι → ι
.
Inj1
(
x6
(
λ x9 x10 .
Inj1
(
setsum
0
0
)
)
(
λ x9 :
ι → ι
.
x8
0
(
λ x10 .
setsum
0
0
)
0
)
(
Inj0
0
)
)
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→ ι
.
∀ x5 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
∀ x6 .
∀ x7 :
(
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
ι →
ι → ι
)
→
ι →
ι → ι
.
x2
(
λ x8 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
λ x9 .
Inj0
0
)
0
⟶
x0
(
λ x8 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x9 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 x11 x12 .
setsum
x10
x11
)
(
λ x8 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x9 .
λ x10 :
ι → ι
.
setsum
(
x8
(
x7
(
λ x11 x12 :
ι → ι
.
λ x13 .
setsum
0
0
)
(
λ x11 x12 .
setsum
0
0
)
(
setsum
0
0
)
(
x8
0
(
λ x11 .
0
)
0
)
)
(
λ x11 .
Inj1
0
)
(
Inj1
(
setsum
0
0
)
)
)
0
)
(
x4
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 x10 .
0
)
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
ι →
(
ι → ι
)
→ ι
.
∀ x7 :
(
ι →
ι → ι
)
→
ι → ι
.
x0
(
λ x8 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x9 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 x11 x12 .
0
)
(
λ x8 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x9 .
λ x10 :
ι → ι
.
setsum
(
Inj1
(
Inj0
x9
)
)
x9
)
(
Inj0
(
Inj1
(
Inj0
x4
)
)
)
⟶
x0
(
λ x8 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x9 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 x11 x12 .
x11
)
(
λ x8 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x9 .
λ x10 :
ι → ι
.
Inj1
(
x8
(
Inj0
0
)
(
λ x11 .
Inj0
(
x10
0
)
)
(
Inj0
(
Inj1
0
)
)
)
)
(
Inj1
(
x7
(
λ x8 x9 .
setsum
(
setsum
0
0
)
x8
)
0
)
)
)
⟶
False
)
Known
3311e..
:
not
(
∀ x0 :
(
ι → ι
)
→
ι → ο
.
∀ x1 x2 :
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ο
.
∀ x3 :
(
ι →
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι →
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→ ο
.
(
∀ x4 x5 x6 x7 .
In
(
setsum
(
setsum
(
setsum
(
Inj1
0
)
0
)
(
Inj0
(
Inj0
0
)
)
)
(
setsum
(
setsum
0
0
)
(
Inj0
(
setsum
0
0
)
)
)
)
(
setsum
(
setsum
(
setsum
(
setsum
0
0
)
x4
)
x7
)
0
)
⟶
x1
(
λ x8 :
ι → ι
.
setsum
(
setsum
(
Inj0
x5
)
(
Inj0
0
)
)
0
)
(
Inj0
(
setsum
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
(
Inj0
(
Inj0
0
)
)
)
)
(
setsum
(
Inj0
(
setsum
0
(
Inj1
0
)
)
)
0
)
⟶
x3
(
λ x8 .
λ x9 :
(
ι → ι
)
→ ι
.
x9
(
λ x10 .
x8
)
)
x5
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 .
Inj0
0
)
)
⟶
(
∀ x4 :
ι →
ι → ι
.
∀ x5 .
∀ x6 :
ι →
ι → ι
.
∀ x7 :
ι →
(
ι →
ι → ι
)
→ ι
.
x3
(
λ x8 .
λ x9 :
(
ι → ι
)
→ ι
.
setsum
(
x9
(
λ x10 .
setsum
(
setsum
0
0
)
x8
)
)
0
)
0
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 .
setsum
(
x8
(
λ x10 .
x8
(
λ x11 .
setsum
0
0
)
)
)
0
)
⟶
False
)
⟶
(
∀ x4 .
∀ x5 :
ι →
(
ι → ι
)
→ ι
.
∀ x6 :
ι → ι
.
∀ x7 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→
ι → ι
.
x0
(
λ x8 .
0
)
(
x6
(
Inj0
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
)
⟶
x2
(
λ x8 :
ι → ι
.
setsum
(
setsum
(
x8
0
)
0
)
(
x7
(
λ x9 .
0
)
(
λ x9 x10 .
setsum
(
Inj0
0
)
0
)
(
x6
(
Inj0
0
)
)
)
)
0
(
x7
(
λ x8 .
Inj1
(
x5
0
(
λ x9 .
0
)
)
)
(
λ x8 x9 .
x8
)
0
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x6 x7 .
x2
(
λ x8 :
ι → ι
.
x6
)
(
setsum
(
setsum
x4
x7
)
(
setsum
0
0
)
)
(
Inj0
0
)
⟶
x0
(
λ x8 .
Inj0
(
x5
0
(
λ x9 :
ι → ι
.
λ x10 .
Inj1
(
Inj0
0
)
)
(
λ x9 .
0
)
)
)
(
setsum
x6
(
Inj0
(
Inj0
(
Inj1
0
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 :
(
ι → ι
)
→
ι → ι
.
∀ x7 .
x0
(
λ x8 .
0
)
(
Inj1
x4
)
⟶
x1
(
λ x8 :
ι → ι
.
setsum
0
(
Inj0
(
Inj1
(
Inj1
0
)
)
)
)
x4
(
setsum
0
0
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 .
∀ x6 :
ι →
(
ι → ι
)
→ ι
.
∀ x7 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι →
ι →
ι → ι
.
x1
(
λ x8 :
ι → ι
.
setsum
0
x5
)
(
setsum
(
Inj1
0
)
(
setsum
(
Inj0
(
setsum
0
0
)
)
0
)
)
(
Inj1
(
x7
(
λ x8 :
(
ι → ι
)
→ ι
.
x6
(
Inj0
0
)
(
λ x9 .
Inj1
0
)
)
(
Inj1
(
Inj0
0
)
)
(
Inj0
(
setsum
0
0
)
)
0
)
)
⟶
In
(
Inj0
(
Inj0
(
x7
(
λ x8 :
(
ι → ι
)
→ ι
.
x8
(
λ x9 .
0
)
)
x5
(
Inj1
0
)
(
Inj0
0
)
)
)
)
(
x4
x5
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
ι →
ι → ι
.
∀ x7 .
In
(
setsum
x7
(
setsum
0
0
)
)
(
Inj0
x7
)
⟶
x0
(
λ x8 .
x8
)
(
Inj1
0
)
⟶
x0
(
λ x8 .
x6
0
(
setsum
0
(
Inj0
0
)
)
)
(
setsum
(
setsum
(
Inj1
x5
)
0
)
(
setsum
(
x6
0
x4
)
(
setsum
(
Inj1
0
)
(
x6
0
0
)
)
)
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
(
ι → ι
)
→ ι
.
∀ x7 :
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
x0
(
λ x8 .
x6
(
λ x9 .
Inj1
0
)
)
(
Inj1
(
setsum
0
(
Inj1
(
setsum
0
0
)
)
)
)
⟶
False
)
⟶
False
)
Known
63b62..
:
not
(
∀ x0 :
(
ι →
(
ι →
(
ι → ι
)
→ ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→ ο
.
∀ x1 :
(
(
ι →
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
(
ι →
ι → ι
)
→ ι
)
→
ι → ι
)
→
ι →
ι →
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ο
.
∀ x2 :
(
ι →
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
)
→
ι →
ι →
ι →
(
ι → ι
)
→
ι → ο
.
∀ x3 :
(
ι →
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
(
(
(
ι →
ι → ι
)
→ ι
)
→ ι
)
→
(
ι → ι
)
→ ο
.
(
∀ x4 :
ι →
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x5 x6 .
∀ x7 :
(
ι → ι
)
→
ι →
ι → ι
.
In
(
Inj0
x6
)
(
setsum
0
(
setsum
0
0
)
)
⟶
x2
(
λ x8 .
λ x9 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
Inj1
x6
)
(
setsum
(
Inj0
(
Inj1
(
setsum
0
0
)
)
)
(
Inj0
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
)
(
x7
(
λ x8 .
setsum
0
0
)
0
0
)
(
setsum
(
x7
(
setsum
x6
)
(
Inj1
(
Inj1
0
)
)
0
)
x5
)
(
λ x8 .
0
)
(
x7
(
λ x8 .
Inj0
0
)
(
x4
(
setsum
(
Inj1
0
)
(
Inj0
0
)
)
(
λ x8 .
x6
)
(
λ x8 .
0
)
0
)
(
Inj0
(
setsum
x5
(
Inj1
0
)
)
)
)
⟶
x3
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 :
ι → ι
.
0
)
(
λ x8 :
(
ι →
ι → ι
)
→ ι
.
x6
)
(
λ x8 .
x5
)
)
⟶
(
∀ x4 :
(
(
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
ι →
ι →
ι → ι
.
∀ x5 x6 .
∀ x7 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
x3
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 :
ι → ι
.
x11
0
)
(
λ x8 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x8 .
0
)
⟶
x2
(
λ x8 .
λ x9 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
Inj0
(
x7
0
(
Inj0
0
)
(
λ x10 .
0
)
(
Inj0
(
setsum
0
0
)
)
)
)
x6
(
x4
(
λ x8 x9 :
ι → ι
.
0
)
(
x4
(
λ x8 x9 :
ι → ι
.
0
)
(
Inj0
(
Inj0
0
)
)
0
0
)
(
setsum
(
setsum
0
x6
)
(
setsum
(
Inj0
0
)
(
Inj1
0
)
)
)
x6
)
x6
(
λ x8 .
setsum
(
Inj1
(
setsum
(
x7
0
0
(
λ x9 .
0
)
0
)
(
setsum
0
0
)
)
)
(
setsum
(
setsum
0
(
setsum
0
0
)
)
(
setsum
x8
(
Inj0
0
)
)
)
)
(
Inj1
(
x7
(
setsum
(
setsum
0
0
)
0
)
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
(
λ x8 .
Inj0
(
Inj1
0
)
)
0
)
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→ ι
.
∀ x5 x6 x7 .
In
x7
(
setsum
(
Inj0
(
x4
(
λ x8 .
0
)
)
)
0
)
⟶
x2
(
λ x8 .
λ x9 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
(
x4
(
λ x8 .
x5
)
)
(
Inj1
(
Inj0
(
setsum
(
Inj1
0
)
0
)
)
)
(
Inj0
0
)
(
λ x8 .
Inj1
0
)
(
Inj0
(
Inj0
0
)
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
∀ x5 x6 x7 .
x2
(
λ x8 .
λ x9 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
x6
0
x7
(
λ x8 .
setsum
0
(
Inj0
(
Inj1
(
Inj1
0
)
)
)
)
(
x4
(
λ x8 .
0
)
(
λ x8 :
ι → ι
.
Inj1
x6
)
(
setsum
0
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
)
⟶
x3
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 :
ι → ι
.
0
)
(
λ x8 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x8 .
setsum
x5
0
)
)
⟶
(
∀ x4 :
ι →
ι →
ι →
ι → ι
.
∀ x5 .
∀ x6 :
ι →
ι →
ι → ι
.
∀ x7 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
x3
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 :
ι → ι
.
setsum
(
Inj0
(
Inj1
(
x11
0
)
)
)
(
x9
0
)
)
(
λ x8 :
(
ι →
ι → ι
)
→ ι
.
0
)
Inj0
⟶
x1
(
λ x8 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
ι →
ι → ι
)
→ ι
.
λ x10 .
setsum
(
x7
(
x9
(
λ x11 x12 .
setsum
0
0
)
)
(
λ x11 :
ι → ι
.
x10
)
)
0
)
(
Inj1
0
)
x5
(
λ x8 :
ι → ι
.
λ x9 .
0
)
(
λ x8 .
0
)
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 x7 .
x1
(
λ x8 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
ι →
ι → ι
)
→ ι
.
λ x10 .
setsum
(
x9
(
λ x11 x12 .
0
)
)
(
x8
0
(
λ x11 :
ι → ι
.
Inj0
(
x11
0
)
)
)
)
(
Inj0
(
setsum
(
Inj1
0
)
(
setsum
x4
(
setsum
0
0
)
)
)
)
(
setsum
x7
(
Inj1
(
setsum
(
setsum
0
0
)
0
)
)
)
(
λ x8 :
ι → ι
.
λ x9 .
x7
)
(
λ x8 .
0
)
⟶
x1
(
λ x8 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
ι →
ι → ι
)
→ ι
.
λ x10 .
x10
)
(
Inj0
x7
)
0
(
λ x8 :
ι → ι
.
λ x9 .
0
)
(
λ x8 .
x8
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
ι →
ι → ι
.
∀ x7 .
x0
(
λ x8 .
λ x9 :
ι →
(
ι → ι
)
→ ι
.
Inj0
(
Inj1
(
Inj1
(
setsum
0
0
)
)
)
)
(
λ x8 :
ι → ι
.
0
)
⟶
x0
(
λ x8 .
λ x9 :
ι →
(
ι → ι
)
→ ι
.
setsum
(
Inj1
(
Inj1
(
setsum
0
0
)
)
)
(
setsum
(
x9
0
(
λ x10 .
setsum
0
0
)
)
x7
)
)
(
λ x8 :
ι → ι
.
setsum
0
(
x6
(
x6
0
0
)
x5
)
)
)
⟶
(
∀ x4 :
ι →
ι → ι
.
∀ x5 :
ι → ι
.
∀ x6 .
∀ x7 :
ι → ι
.
In
x6
(
x5
(
setsum
(
x4
0
(
Inj1
0
)
)
(
x4
x6
(
Inj0
0
)
)
)
)
⟶
x0
(
λ x8 .
λ x9 :
ι →
(
ι → ι
)
→ ι
.
setsum
(
x9
0
(
λ x10 .
0
)
)
(
x9
(
Inj1
(
x9
0
(
λ x10 .
0
)
)
)
(
λ x10 .
x8
)
)
)
(
λ x8 :
ι → ι
.
x8
0
)
⟶
x1
(
λ x8 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
ι →
ι → ι
)
→ ι
.
λ x10 .
setsum
(
setsum
(
Inj0
(
Inj1
0
)
)
(
Inj1
(
setsum
0
0
)
)
)
(
x8
(
setsum
(
x9
(
λ x11 x12 .
0
)
)
(
setsum
0
0
)
)
(
λ x11 :
ι → ι
.
x8
(
setsum
0
0
)
(
λ x12 :
ι → ι
.
x10
)
)
)
)
(
x4
(
x4
(
x4
(
setsum
0
0
)
(
Inj1
0
)
)
(
x7
0
)
)
(
setsum
(
setsum
(
x4
0
0
)
(
setsum
0
0
)
)
0
)
)
(
x5
(
x4
(
setsum
0
(
x5
0
)
)
0
)
)
(
λ x8 :
ι → ι
.
λ x9 .
Inj0
(
setsum
(
Inj1
(
Inj0
0
)
)
0
)
)
(
λ x8 .
Inj1
(
setsum
(
x7
(
setsum
0
0
)
)
(
Inj1
x6
)
)
)
)
⟶
False
)
Known
bfeb0..
:
not
(
∀ x0 :
(
ι → ι
)
→
ι →
(
ι → ι
)
→ ο
.
∀ x1 :
(
(
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι →
(
ι → ι
)
→ ι
)
→ ο
.
∀ x2 :
(
(
ι → ι
)
→
ι →
(
ι → ι
)
→ ι
)
→
ι → ο
.
∀ x3 :
(
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
ι → ο
.
(
∀ x4 :
ι → ι
.
∀ x5 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x6 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
.
∀ x7 .
In
(
Inj1
0
)
x7
⟶
x3
(
λ x8 :
ι →
(
ι → ι
)
→ ι
.
λ x9 .
Inj1
0
)
(
Inj0
0
)
)
⟶
(
∀ x4 :
ι →
ι →
ι → ι
.
∀ x5 :
ι →
(
ι →
ι → ι
)
→ ι
.
∀ x6 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
∀ x7 .
In
(
setsum
(
x4
(
setsum
x7
(
x6
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
0
)
0
(
λ x8 .
0
)
0
)
)
(
Inj1
(
Inj1
0
)
)
0
)
(
Inj1
0
)
)
(
Inj0
x7
)
⟶
x3
(
λ x8 :
ι →
(
ι → ι
)
→ ι
.
λ x9 .
Inj1
(
setsum
0
(
Inj1
x7
)
)
)
(
x6
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
setsum
(
setsum
x10
0
)
(
Inj1
(
setsum
0
0
)
)
)
(
Inj0
(
x4
0
0
(
setsum
0
0
)
)
)
(
λ x8 .
Inj0
0
)
(
Inj1
0
)
)
⟶
x3
(
λ x8 :
ι →
(
ι → ι
)
→ ι
.
λ x9 .
setsum
(
Inj0
(
x8
x9
(
λ x10 .
Inj0
0
)
)
)
(
Inj1
x9
)
)
(
setsum
(
setsum
(
x5
(
setsum
0
0
)
(
λ x8 x9 .
setsum
0
0
)
)
(
setsum
(
setsum
0
0
)
(
x6
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
0
)
0
(
λ x8 .
0
)
0
)
)
)
x7
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
(
ι →
ι → ι
)
→ ι
.
∀ x7 :
ι → ι
.
x2
(
λ x8 :
ι → ι
.
λ x9 .
λ x10 :
ι → ι
.
setsum
(
setsum
(
setsum
0
(
setsum
0
0
)
)
(
x10
0
)
)
0
)
0
)
⟶
(
∀ x4 :
ι →
ι → ι
.
∀ x5 .
∀ x6 :
(
ι →
ι →
ι → ι
)
→ ι
.
∀ x7 .
x2
(
λ x8 :
ι → ι
.
λ x9 .
λ x10 :
ι → ι
.
x10
(
setsum
(
setsum
(
setsum
0
0
)
0
)
(
x10
(
Inj0
0
)
)
)
)
(
setsum
0
(
setsum
(
x4
(
Inj0
0
)
x5
)
(
Inj1
0
)
)
)
⟶
x2
(
λ x8 :
ι → ι
.
λ x9 .
λ x10 :
ι → ι
.
x8
(
setsum
x7
(
Inj0
x7
)
)
)
(
Inj0
(
setsum
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
(
Inj0
(
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 .
∀ x6 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
∀ x7 .
x1
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→ ι
.
λ x9 .
0
)
(
λ x8 :
ι → ι
.
λ x9 .
λ x10 :
ι → ι
.
0
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
ι →
ι → ι
.
∀ x7 :
(
ι → ι
)
→
(
ι → ι
)
→
ι →
ι → ι
.
In
x5
(
Inj0
(
Inj0
(
x7
(
λ x8 .
x7
(
λ x9 .
0
)
(
λ x9 .
0
)
0
0
)
(
λ x8 .
0
)
(
Inj0
0
)
(
Inj0
0
)
)
)
)
⟶
x1
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→ ι
.
λ x9 .
x6
(
setsum
(
Inj0
(
x6
0
0
)
)
(
setsum
0
0
)
)
(
Inj0
(
x6
(
Inj0
0
)
0
)
)
)
(
λ x8 :
ι → ι
.
λ x9 .
λ x10 :
ι → ι
.
setsum
0
x9
)
⟶
x3
(
λ x8 :
ι →
(
ι → ι
)
→ ι
.
λ x9 .
x7
(
λ x10 .
x10
)
(
λ x10 .
x8
(
Inj0
(
x8
0
(
λ x11 .
0
)
)
)
(
λ x11 .
setsum
x11
(
setsum
0
0
)
)
)
(
setsum
0
(
setsum
(
x7
(
λ x10 .
0
)
(
λ x10 .
0
)
0
0
)
(
Inj0
0
)
)
)
(
setsum
x9
0
)
)
(
Inj1
(
x7
(
λ x8 .
0
)
(
λ x8 .
setsum
(
setsum
0
0
)
(
Inj0
0
)
)
(
x7
(
λ x8 .
Inj0
0
)
(
λ x8 .
Inj0
0
)
(
Inj1
0
)
(
setsum
0
0
)
)
(
x6
(
x6
0
0
)
0
)
)
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→ ι
.
∀ x5 .
∀ x6 :
ι →
ι → ι
.
∀ x7 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
In
(
Inj0
0
)
(
setsum
(
Inj0
(
setsum
(
Inj1
0
)
(
x6
0
0
)
)
)
0
)
⟶
x0
(
setsum
x5
)
(
Inj0
(
x7
(
setsum
(
Inj0
0
)
(
x6
0
0
)
)
(
λ x8 :
ι → ι
.
λ x9 .
setsum
(
Inj0
0
)
0
)
)
)
(
λ x8 .
x6
x5
(
setsum
(
Inj0
x5
)
(
x6
x8
(
setsum
0
0
)
)
)
)
⟶
x0
(
λ x8 .
0
)
(
x4
(
λ x8 .
x5
)
)
(
λ x8 .
Inj0
(
setsum
x5
(
x6
(
setsum
0
0
)
(
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι →
(
ι → ι
)
→ ι
.
∀ x6 x7 :
ι → ι
.
x0
(
λ x8 .
Inj1
(
Inj0
(
x5
(
λ x9 :
(
ι → ι
)
→ ι
.
Inj0
0
)
(
x6
0
)
(
λ x9 .
setsum
0
0
)
)
)
)
(
setsum
0
(
Inj1
0
)
)
(
λ x8 .
0
)
⟶
x0
(
λ x8 .
x5
(
λ x9 :
(
ι → ι
)
→ ι
.
0
)
x8
(
λ x9 .
0
)
)
(
Inj1
(
Inj1
(
x7
0
)
)
)
(
λ x8 .
setsum
(
setsum
(
Inj0
(
x7
0
)
)
(
Inj0
0
)
)
(
Inj1
(
Inj0
(
x7
0
)
)
)
)
)
⟶
False
)
Known
ebfdd..
:
not
(
∀ x0 :
(
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι →
(
(
ι → ι
)
→ ι
)
→
ι → ο
.
∀ x1 :
(
ι →
(
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι →
ι →
ι → ι
)
→
ι →
(
ι →
(
ι → ι
)
→ ι
)
→ ο
.
∀ x2 :
(
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
)
→
ι →
ι → ο
.
∀ x3 :
(
(
ι →
ι →
(
ι → ι
)
→ ι
)
→
ι →
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
)
→
(
(
ι →
ι →
ι → ι
)
→ ι
)
→
ι → ο
.
(
∀ x4 :
ι → ι
.
∀ x5 :
(
(
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
∀ x6 x7 .
x3
(
λ x8 :
ι →
ι →
(
ι → ι
)
→ ι
.
λ x9 .
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 x12 .
Inj1
(
Inj0
x11
)
)
(
λ x8 :
ι →
ι →
ι → ι
.
setsum
x6
(
Inj1
(
Inj0
(
setsum
0
0
)
)
)
)
(
Inj0
(
setsum
(
setsum
(
x4
0
)
0
)
0
)
)
)
⟶
(
∀ x4 :
ι →
(
ι → ι
)
→ ι
.
∀ x5 .
∀ x6 :
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
∀ x7 .
In
(
setsum
0
x5
)
(
setsum
(
Inj0
0
)
(
Inj1
0
)
)
⟶
x3
(
λ x8 :
ι →
ι →
(
ι → ι
)
→ ι
.
λ x9 .
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 x12 .
setsum
(
Inj0
x11
)
(
Inj0
(
Inj0
(
x10
(
λ x13 .
0
)
0
)
)
)
)
(
λ x8 :
ι →
ι →
ι → ι
.
0
)
0
⟶
x3
(
λ x8 :
ι →
ι →
(
ι → ι
)
→ ι
.
λ x9 .
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 x12 .
setsum
0
(
Inj1
(
setsum
(
Inj1
0
)
0
)
)
)
(
λ x8 :
ι →
ι →
ι → ι
.
x5
)
(
setsum
x7
(
Inj0
(
Inj0
0
)
)
)
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
ι → ι
.
x3
(
λ x8 :
ι →
ι →
(
ι → ι
)
→ ι
.
λ x9 .
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 x12 .
x11
)
(
λ x8 :
ι →
ι →
ι → ι
.
x5
)
(
Inj0
x5
)
⟶
x2
(
λ x8 .
x7
x5
)
(
λ x8 :
ι → ι
.
0
)
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 :
ι → ι
.
setsum
(
x8
(
λ x10 .
Inj1
(
setsum
0
0
)
)
)
(
setsum
(
setsum
(
x8
(
λ x10 .
0
)
)
(
x7
0
)
)
(
Inj0
(
Inj0
0
)
)
)
)
(
Inj1
(
Inj1
(
setsum
x5
(
Inj1
0
)
)
)
)
(
setsum
(
Inj1
(
setsum
(
setsum
0
0
)
x5
)
)
(
setsum
(
Inj1
x6
)
(
Inj1
(
Inj1
0
)
)
)
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x5 x6 x7 .
In
(
Inj0
x5
)
(
Inj1
(
Inj1
(
Inj0
0
)
)
)
⟶
x2
(
λ x8 .
x6
)
(
λ x8 :
ι → ι
.
Inj0
(
Inj0
0
)
)
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 :
ι → ι
.
0
)
(
Inj1
(
setsum
0
(
Inj0
0
)
)
)
x5
⟶
x2
(
λ x8 .
0
)
(
λ x8 :
ι → ι
.
x5
)
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 :
ι → ι
.
Inj1
0
)
(
Inj1
x5
)
x6
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 :
(
ι →
ι →
ι → ι
)
→
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x7 .
In
(
setsum
(
Inj1
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
(
setsum
(
Inj0
(
x5
0
)
)
0
)
)
(
Inj1
(
setsum
(
setsum
(
Inj1
0
)
(
setsum
0
0
)
)
(
Inj0
(
x6
(
λ x8 x9 x10 .
0
)
(
λ x8 .
0
)
(
λ x8 .
0
)
)
)
)
)
⟶
x0
(
λ x8 x9 .
setsum
(
setsum
0
0
)
(
x6
(
λ x10 x11 x12 .
Inj0
(
Inj1
0
)
)
(
λ x10 .
0
)
(
λ x10 .
x8
)
)
)
(
λ x8 :
ι → ι
.
Inj0
(
setsum
(
x6
(
λ x9 x10 x11 .
Inj0
0
)
(
λ x9 .
0
)
(
λ x9 .
Inj0
0
)
)
0
)
)
(
Inj0
(
setsum
(
setsum
(
setsum
0
0
)
0
)
(
Inj0
(
setsum
0
0
)
)
)
)
(
λ x8 :
ι → ι
.
Inj0
(
setsum
0
0
)
)
(
setsum
x7
(
Inj0
(
Inj0
0
)
)
)
⟶
x1
(
λ x8 .
λ x9 :
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x10 x11 x12 .
x11
)
(
Inj1
(
setsum
(
Inj0
0
)
0
)
)
(
λ x8 .
λ x9 :
ι → ι
.
0
)
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 x7 .
In
(
Inj0
0
)
(
Inj1
(
setsum
0
(
Inj0
x6
)
)
)
⟶
x1
(
λ x8 .
λ x9 :
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x10 x11 x12 .
0
)
0
(
λ x8 .
λ x9 :
ι → ι
.
x9
(
setsum
0
(
Inj1
x7
)
)
)
⟶
x1
(
λ x8 .
λ x9 :
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x10 x11 x12 .
setsum
(
setsum
0
(
Inj0
(
Inj0
0
)
)
)
(
Inj1
(
x9
(
λ x13 .
setsum
0
0
)
(
λ x13 .
x13
)
x11
)
)
)
x6
(
λ x8 .
λ x9 :
ι → ι
.
setsum
(
setsum
0
0
)
0
)
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 x7 .
In
(
x5
0
)
(
setsum
(
Inj0
(
setsum
0
(
x5
0
)
)
)
(
setsum
x7
(
setsum
(
setsum
0
0
)
0
)
)
)
⟶
x0
(
λ x8 x9 .
0
)
(
λ x8 :
ι → ι
.
x8
(
setsum
(
x8
(
x5
0
)
)
(
Inj0
0
)
)
)
(
Inj1
x6
)
(
λ x8 :
ι → ι
.
Inj1
(
setsum
(
setsum
(
x8
0
)
x6
)
(
Inj1
(
setsum
0
0
)
)
)
)
0
)
⟶
(
∀ x4 .
∀ x5 :
(
ι → ι
)
→ ι
.
∀ x6 .
∀ x7 :
ι → ι
.
x0
(
λ x8 x9 .
x8
)
(
λ x8 :
ι → ι
.
setsum
0
(
setsum
0
(
x7
(
x5
(
λ x9 .
0
)
)
)
)
)
0
(
λ x8 :
ι → ι
.
Inj1
(
Inj0
0
)
)
(
x7
0
)
⟶
x0
(
λ x8 x9 .
0
)
(
λ x8 :
ι → ι
.
x8
0
)
(
setsum
(
setsum
0
(
Inj1
(
Inj1
0
)
)
)
0
)
(
λ x8 :
ι → ι
.
0
)
(
Inj0
(
Inj1
0
)
)
)
⟶
False
)
Known
7a4d9..
:
not
(
∀ x0 :
(
ι →
(
ι → ι
)
→ ι
)
→
(
(
ι →
(
ι → ι
)
→ ι
)
→ ι
)
→ ο
.
∀ x1 :
(
ι →
(
ι → ι
)
→
ι →
ι → ι
)
→
(
(
ι →
(
ι → ι
)
→
ι → ι
)
→
ι →
ι →
ι → ι
)
→
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ο
.
∀ x2 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ο
.
∀ x3 :
(
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→ ι
)
→
ι → ο
.
(
∀ x4 :
ι → ι
.
∀ x5 x6 .
∀ x7 :
ι → ι
.
x0
(
λ x8 .
λ x9 :
ι → ι
.
0
)
(
λ x8 :
ι →
(
ι → ι
)
→ ι
.
setsum
0
x5
)
⟶
x3
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
x8
(
λ x9 :
ι → ι
.
Inj1
0
)
x6
)
(
setsum
(
Inj0
0
)
(
setsum
(
Inj1
(
x4
0
)
)
(
Inj1
(
Inj0
0
)
)
)
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x5 :
ι →
(
ι → ι
)
→
ι → ι
.
∀ x6 :
ι →
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
∀ x7 .
x3
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
x8
(
λ x9 :
ι → ι
.
Inj0
x7
)
0
)
(
Inj1
x7
)
⟶
False
)
⟶
(
∀ x4 .
∀ x5 :
(
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x6 :
(
ι →
ι → ι
)
→ ι
.
∀ x7 .
x2
(
λ x8 :
ι → ι
.
λ x9 .
setsum
(
x8
(
setsum
0
(
setsum
0
0
)
)
)
x7
)
(
λ x8 .
λ x9 :
(
ι → ι
)
→
ι → ι
.
x6
(
λ x10 x11 .
setsum
(
setsum
x11
(
setsum
0
0
)
)
x11
)
)
⟶
x2
(
λ x8 :
ι → ι
.
λ x9 .
0
)
(
λ x8 .
λ x9 :
(
ι → ι
)
→
ι → ι
.
Inj1
(
Inj1
0
)
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→ ι
.
∀ x5 x6 x7 .
x2
(
λ x8 :
ι → ι
.
Inj1
)
(
λ x8 .
λ x9 :
(
ι → ι
)
→
ι → ι
.
0
)
⟶
False
)
⟶
(
∀ x4 :
ι →
ι →
ι →
ι → ι
.
∀ x5 x6 .
∀ x7 :
ι → ι
.
In
(
Inj1
0
)
(
setsum
(
Inj0
(
x4
(
setsum
0
0
)
(
Inj1
0
)
(
Inj1
0
)
(
setsum
0
0
)
)
)
0
)
⟶
x1
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 x11 .
setsum
(
Inj1
(
setsum
0
(
Inj1
0
)
)
)
(
x9
(
Inj1
0
)
)
)
(
λ x8 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x9 x10 x11 .
x11
)
(
λ x8 :
(
ι → ι
)
→ ι
.
0
)
⟶
x1
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 x11 .
0
)
(
λ x8 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x9 x10 x11 .
setsum
(
setsum
0
(
Inj0
0
)
)
(
setsum
(
Inj0
0
)
0
)
)
(
λ x8 :
(
ι → ι
)
→ ι
.
setsum
(
Inj0
(
x7
(
setsum
0
0
)
)
)
0
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 x6 x7 .
x1
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 x11 .
setsum
(
Inj0
(
setsum
(
setsum
0
0
)
(
Inj0
0
)
)
)
(
setsum
(
setsum
(
setsum
0
0
)
0
)
(
Inj1
0
)
)
)
(
λ x8 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x9 x10 x11 .
0
)
(
λ x8 :
(
ι → ι
)
→ ι
.
setsum
0
(
Inj0
x6
)
)
⟶
In
(
Inj1
(
Inj1
0
)
)
x7
)
⟶
(
∀ x4 x5 :
ι →
ι → ι
.
∀ x6 x7 .
x0
(
λ x8 .
λ x9 :
ι → ι
.
0
)
(
λ x8 :
ι →
(
ι → ι
)
→ ι
.
x7
)
⟶
x0
(
λ x8 .
λ x9 :
ι → ι
.
x6
)
(
λ x8 :
ι →
(
ι → ι
)
→ ι
.
0
)
)
⟶
(
∀ x4 :
ι →
ι → ι
.
∀ x5 .
∀ x6 x7 :
ι → ι
.
x0
(
λ x8 .
λ x9 :
ι → ι
.
Inj0
(
setsum
0
(
Inj1
0
)
)
)
(
λ x8 :
ι →
(
ι → ι
)
→ ι
.
0
)
⟶
In
(
setsum
0
0
)
(
Inj0
0
)
)
⟶
False
)
Known
9033d..
:
not
(
∀ x0 :
(
(
ι →
ι →
(
ι → ι
)
→ ι
)
→ ι
)
→
ι →
ι → ο
.
∀ x1 :
(
ι → ι
)
→
ι → ο
.
∀ x2 :
(
(
(
(
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
)
→
ι →
(
ι →
ι → ι
)
→ ο
.
∀ x3 :
(
ι →
(
ι → ι
)
→ ι
)
→
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ο
.
(
∀ x4 :
ι →
ι →
ι →
ι → ι
.
∀ x5 x6 .
∀ x7 :
ι → ι
.
x3
(
λ x8 .
λ x9 :
ι → ι
.
x9
(
Inj1
(
Inj0
x6
)
)
)
(
λ x8 :
(
ι → ι
)
→ ι
.
setsum
(
Inj1
(
setsum
x6
0
)
)
(
Inj0
0
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
∀ x6 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→ ι
.
∀ x7 .
In
(
setsum
(
Inj0
(
setsum
(
Inj0
0
)
0
)
)
(
Inj1
0
)
)
(
Inj0
x7
)
⟶
x3
(
λ x8 .
λ x9 :
ι → ι
.
x8
)
(
λ x8 :
(
ι → ι
)
→ ι
.
Inj0
(
setsum
(
setsum
(
setsum
0
0
)
0
)
(
setsum
(
setsum
0
0
)
0
)
)
)
⟶
x3
(
λ x8 .
λ x9 :
ι → ι
.
0
)
(
λ x8 :
(
ι → ι
)
→ ι
.
0
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
ι →
ι → ι
.
∀ x7 :
(
ι → ι
)
→
ι → ι
.
x1
(
λ x8 .
x5
)
(
setsum
x5
(
x6
(
Inj1
0
)
(
Inj1
(
Inj0
0
)
)
)
)
⟶
x2
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
x6
(
x8
(
λ x9 :
ι → ι
.
0
)
(
λ x9 :
ι → ι
.
λ x10 .
0
)
)
0
)
(
x6
0
x4
)
(
λ x8 x9 .
Inj1
(
x7
(
λ x10 .
Inj1
x9
)
0
)
)
)
⟶
(
∀ x4 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
∀ x5 x6 x7 .
x2
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
Inj1
0
)
0
(
λ x8 x9 .
setsum
(
Inj0
0
)
x7
)
⟶
In
(
Inj0
(
Inj0
(
setsum
x6
(
Inj0
0
)
)
)
)
(
Inj0
(
setsum
(
Inj0
(
setsum
0
0
)
)
(
setsum
(
x4
0
0
(
λ x8 .
0
)
0
)
x7
)
)
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
(
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
∀ x7 .
In
(
Inj1
x5
)
(
Inj1
(
setsum
(
Inj1
(
x6
(
λ x8 x9 :
ι → ι
.
λ x10 .
0
)
(
λ x8 x9 .
0
)
)
)
(
Inj1
(
setsum
0
0
)
)
)
)
⟶
x1
(
λ x8 .
x6
(
λ x9 x10 :
ι → ι
.
λ x11 .
Inj0
0
)
(
λ x9 x10 .
setsum
(
Inj0
0
)
0
)
)
(
setsum
0
(
setsum
(
setsum
0
(
setsum
0
0
)
)
(
setsum
0
0
)
)
)
⟶
x1
(
λ x8 .
0
)
(
setsum
0
(
Inj0
0
)
)
)
⟶
(
∀ x4 .
∀ x5 :
(
ι → ι
)
→
ι → ι
.
∀ x6 x7 .
x1
(
λ x8 .
0
)
(
Inj1
(
setsum
(
Inj1
(
setsum
0
0
)
)
(
Inj1
0
)
)
)
⟶
False
)
⟶
(
∀ x4 x5 .
∀ x6 :
ι → ι
.
∀ x7 .
In
x5
(
setsum
(
setsum
0
0
)
(
Inj1
(
setsum
(
Inj0
0
)
x4
)
)
)
⟶
x1
(
λ x8 .
x7
)
(
Inj1
0
)
⟶
x0
(
λ x8 :
ι →
ι →
(
ι → ι
)
→ ι
.
setsum
(
setsum
x7
0
)
(
x6
0
)
)
0
(
setsum
(
Inj0
(
setsum
0
(
Inj0
0
)
)
)
0
)
)
⟶
(
∀ x4 :
ι →
ι → ι
.
∀ x5 .
∀ x6 :
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
∀ x7 .
x0
(
λ x8 :
ι →
ι →
(
ι → ι
)
→ ι
.
0
)
(
setsum
0
(
Inj0
(
setsum
x5
(
Inj1
0
)
)
)
)
(
setsum
(
Inj0
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
(
Inj0
(
Inj1
0
)
)
)
⟶
In
(
Inj1
(
Inj1
(
Inj1
0
)
)
)
(
setsum
0
(
setsum
0
(
Inj1
0
)
)
)
)
⟶
False
)
Known
8e3ed..
:
not
(
∀ x0 :
(
(
ι →
ι → ι
)
→ ι
)
→
ι → ο
.
∀ x1 :
(
ι → ι
)
→
(
(
(
ι →
ι → ι
)
→
ι → ι
)
→ ι
)
→ ο
.
∀ x2 :
(
ι →
(
ι →
ι →
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
(
ι → ι
)
→
ι →
ι → ο
.
∀ x3 :
(
ι →
(
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
(
ι → ι
)
→
ι →
ι → ι
)
→ ο
.
(
∀ x4 .
∀ x5 :
(
ι →
ι → ι
)
→ ι
.
∀ x6 x7 .
x3
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 :
(
ι → ι
)
→ ι
.
0
)
(
λ x8 :
(
ι → ι
)
→ ι
.
0
)
(
λ x8 :
ι → ι
.
λ x9 x10 .
Inj1
(
setsum
(
Inj0
x9
)
0
)
)
)
⟶
(
∀ x4 x5 x6 x7 .
x3
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 :
(
ι → ι
)
→ ι
.
setsum
(
Inj1
0
)
(
setsum
(
Inj0
(
setsum
0
0
)
)
x7
)
)
(
λ x8 :
(
ι → ι
)
→ ι
.
x6
)
(
λ x8 :
ι → ι
.
λ x9 x10 .
x10
)
⟶
x3
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 :
(
ι → ι
)
→ ι
.
Inj1
(
x10
(
λ x11 .
setsum
(
setsum
0
0
)
0
)
)
)
(
λ x8 :
(
ι → ι
)
→ ι
.
0
)
(
λ x8 :
ι → ι
.
λ x9 x10 .
setsum
x10
x7
)
)
⟶
(
∀ x4 :
(
ι →
(
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
∀ x5 x6 x7 .
In
(
x4
(
λ x8 .
λ x9 :
ι → ι
.
x6
)
(
λ x8 :
ι → ι
.
λ x9 .
Inj1
(
Inj0
(
setsum
0
0
)
)
)
(
setsum
0
(
setsum
(
setsum
0
0
)
0
)
)
x5
)
(
setsum
0
(
setsum
(
setsum
(
setsum
0
0
)
0
)
x7
)
)
⟶
x0
(
λ x8 :
ι →
ι → ι
.
x7
)
(
Inj1
(
setsum
x5
(
Inj1
x6
)
)
)
⟶
x2
(
λ x8 .
λ x9 :
ι →
ι →
ι → ι
.
Inj1
0
)
(
λ x8 .
x5
)
(
λ x8 .
0
)
x6
0
)
⟶
(
∀ x4 :
(
ι →
ι → ι
)
→ ι
.
∀ x5 :
ι →
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x6 :
ι → ι
.
∀ x7 .
In
(
x6
(
Inj0
(
setsum
(
Inj1
0
)
(
Inj1
0
)
)
)
)
(
setsum
(
x5
(
x5
0
(
λ x8 :
ι → ι
.
setsum
0
0
)
(
λ x8 .
Inj1
0
)
(
setsum
0
0
)
)
(
λ x8 :
ι → ι
.
setsum
(
x6
0
)
0
)
(
λ x8 .
x5
0
(
λ x9 :
ι → ι
.
0
)
(
λ x9 .
x7
)
(
setsum
0
0
)
)
0
)
(
x4
(
λ x8 x9 .
Inj1
(
setsum
0
0
)
)
)
)
⟶
x2
(
λ x8 .
λ x9 :
ι →
ι →
ι → ι
.
x6
(
Inj1
x7
)
)
(
λ x8 .
x8
)
(
λ x8 .
setsum
0
0
)
(
x5
0
(
λ x8 :
ι → ι
.
x5
0
(
λ x9 :
ι → ι
.
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
(
λ x9 .
Inj1
(
x6
0
)
)
0
)
(
λ x8 .
setsum
(
x5
(
setsum
0
0
)
(
λ x9 :
ι → ι
.
Inj0
0
)
(
λ x9 .
Inj0
0
)
(
Inj1
0
)
)
(
Inj1
0
)
)
(
x4
(
λ x8 x9 .
0
)
)
)
(
x6
0
)
⟶
x0
(
λ x8 :
ι →
ι → ι
.
x5
(
Inj1
0
)
(
λ x9 :
ι → ι
.
Inj0
0
)
Inj1
(
Inj1
0
)
)
(
Inj1
(
x6
(
Inj0
x7
)
)
)
)
⟶
(
∀ x4 :
(
(
ι →
ι → ι
)
→
ι → ι
)
→
ι → ι
.
∀ x5 x6 x7 .
In
x5
x5
⟶
x1
(
λ x8 .
Inj1
x5
)
(
λ x8 :
(
ι →
ι → ι
)
→
ι → ι
.
0
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 x6 .
∀ x7 :
(
ι → ι
)
→ ι
.
In
(
Inj0
(
setsum
(
Inj0
(
Inj1
0
)
)
0
)
)
(
Inj0
(
setsum
(
x4
(
Inj1
0
)
)
x6
)
)
⟶
x1
(
λ x8 .
0
)
(
λ x8 :
(
ι →
ι → ι
)
→
ι → ι
.
x5
)
⟶
x3
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 :
(
ι → ι
)
→ ι
.
setsum
(
Inj1
(
setsum
0
0
)
)
(
Inj1
x8
)
)
(
λ x8 :
(
ι → ι
)
→ ι
.
Inj1
(
setsum
(
Inj1
0
)
0
)
)
(
λ x8 :
ι → ι
.
λ x9 x10 .
x10
)
)
⟶
(
∀ x4 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
∀ x5 .
∀ x6 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x7 :
ι → ι
.
In
(
Inj0
0
)
(
setsum
(
x6
(
setsum
(
setsum
0
0
)
(
Inj1
0
)
)
(
λ x8 :
ι → ι
.
x5
)
)
(
x6
0
(
λ x8 :
ι → ι
.
x5
)
)
)
⟶
x0
(
λ x8 :
ι →
ι → ι
.
0
)
(
setsum
0
(
Inj1
(
setsum
(
Inj0
0
)
(
x4
(
λ x8 :
ι →
ι → ι
.
λ x9 :
ι → ι
.
0
)
(
λ x8 :
ι → ι
.
0
)
0
0
)
)
)
)
)
⟶
(
∀ x4 :
ι →
(
ι → ι
)
→ ι
.
∀ x5 :
ι →
(
ι →
ι → ι
)
→ ι
.
∀ x6 :
ι →
ι → ι
.
∀ x7 .
x0
(
λ x8 :
ι →
ι → ι
.
Inj1
(
setsum
(
setsum
(
setsum
0
0
)
0
)
(
setsum
(
Inj0
0
)
0
)
)
)
0
⟶
x3
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 :
(
ι → ι
)
→ ι
.
setsum
0
(
x10
(
λ x11 .
setsum
0
0
)
)
)
(
λ x8 :
(
ι → ι
)
→ ι
.
Inj0
(
Inj1
(
Inj1
(
setsum
0
0
)
)
)
)
(
λ x8 :
ι → ι
.
λ x9 x10 .
setsum
(
x8
0
)
x7
)
)
⟶
False
)
Known
29cbb..
:
not
(
∀ x0 :
(
ι → ι
)
→
ι → ο
.
∀ x1 :
(
(
(
ι →
ι →
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ο
.
∀ x2 :
(
(
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→ ι
)
→ ι
)
→
(
(
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι →
(
(
ι → ι
)
→ ι
)
→ ο
.
∀ x3 :
(
ι → ι
)
→
ι →
(
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→ ο
.
(
∀ x4 :
ι →
ι → ι
.
∀ x5 :
(
(
ι →
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x6 :
(
ι → ι
)
→ ι
.
∀ x7 .
In
(
setsum
0
(
setsum
(
x6
(
λ x8 .
Inj0
0
)
)
0
)
)
(
setsum
(
x6
(
λ x8 .
Inj0
(
setsum
0
0
)
)
)
(
Inj0
(
setsum
(
setsum
0
0
)
(
x6
(
λ x8 .
0
)
)
)
)
)
⟶
x0
(
λ x8 .
setsum
(
Inj1
(
Inj1
(
setsum
0
0
)
)
)
(
x6
(
λ x9 .
Inj0
x8
)
)
)
(
x4
(
Inj1
(
Inj1
(
Inj0
0
)
)
)
(
setsum
0
(
Inj1
(
x6
(
λ x8 .
0
)
)
)
)
)
⟶
x3
(
λ x8 .
x7
)
(
x5
(
λ x8 :
ι →
ι → ι
.
λ x9 .
setsum
0
(
Inj1
(
x8
0
0
)
)
)
)
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
λ x9 .
setsum
(
Inj1
x7
)
(
x6
(
λ x10 .
x10
)
)
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
.
∀ x5 :
ι →
(
ι → ι
)
→ ι
.
∀ x6 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι → ι
.
∀ x7 .
In
(
x4
(
λ x8 :
(
ι → ι
)
→ ι
.
0
)
)
(
Inj1
(
setsum
(
Inj1
0
)
(
setsum
(
Inj0
0
)
(
setsum
0
0
)
)
)
)
⟶
x3
(
λ x8 .
Inj0
0
)
(
Inj0
(
Inj0
(
x5
0
(
λ x8 .
0
)
)
)
)
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
λ x9 .
0
)
⟶
x0
(
λ x8 .
Inj0
(
Inj0
(
Inj1
x8
)
)
)
(
x6
(
λ x8 :
(
ι → ι
)
→ ι
.
x5
(
setsum
0
0
)
(
setsum
(
Inj0
0
)
)
)
(
setsum
(
x4
(
λ x8 :
(
ι → ι
)
→ ι
.
Inj1
0
)
)
0
)
)
)
⟶
(
∀ x4 :
(
ι →
ι → ι
)
→ ι
.
∀ x5 :
(
(
ι → ι
)
→
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x6 :
(
(
ι → ι
)
→ ι
)
→
ι →
ι →
ι → ι
.
∀ x7 .
x3
(
λ x8 .
Inj1
0
)
0
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
λ x9 .
0
)
⟶
x2
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→ ι
.
0
)
(
λ x8 :
ι →
ι → ι
.
λ x9 :
(
ι → ι
)
→ ι
.
setsum
(
x9
(
λ x10 .
x8
(
setsum
0
0
)
0
)
)
(
setsum
0
0
)
)
(
setsum
(
Inj1
(
Inj0
(
setsum
0
0
)
)
)
(
Inj0
0
)
)
(
λ x8 :
ι → ι
.
x7
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
ι →
ι →
ι → ι
.
∀ x7 .
x2
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→ ι
.
x5
)
(
λ x8 :
ι →
ι → ι
.
λ x9 :
(
ι → ι
)
→ ι
.
0
)
(
Inj1
(
Inj0
0
)
)
(
λ x8 :
ι → ι
.
setsum
(
setsum
(
Inj1
(
x6
0
0
0
)
)
(
setsum
x7
(
x8
0
)
)
)
x5
)
⟶
x3
(
λ x8 .
Inj0
(
Inj1
(
setsum
(
Inj0
0
)
(
setsum
0
0
)
)
)
)
(
x6
0
0
0
)
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
λ x9 .
Inj0
(
Inj1
0
)
)
)
⟶
(
∀ x4 x5 x6 x7 .
x3
(
λ x8 .
setsum
(
setsum
(
setsum
(
Inj1
0
)
0
)
(
Inj1
(
setsum
0
0
)
)
)
0
)
(
setsum
(
setsum
(
setsum
0
(
setsum
0
0
)
)
(
setsum
x5
x4
)
)
(
Inj1
0
)
)
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
λ x9 .
x7
)
⟶
x1
(
λ x8 :
(
ι →
ι →
ι → ι
)
→ ι
.
λ x9 .
Inj1
x7
)
(
λ x8 x9 .
setsum
x6
0
)
(
λ x8 .
0
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 x6 x7 .
x1
(
λ x8 :
(
ι →
ι →
ι → ι
)
→ ι
.
λ x9 .
Inj0
(
Inj0
(
setsum
x7
(
setsum
0
0
)
)
)
)
(
λ x8 x9 .
x7
)
(
λ x8 .
0
)
⟶
x3
(
λ x8 .
0
)
0
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
setsum
(
setsum
0
(
x8
(
λ x9 .
x7
)
0
)
)
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
ι → ι
.
∀ x7 .
x0
(
λ x8 .
x5
)
(
Inj0
0
)
⟶
x0
(
λ x8 .
setsum
x5
(
Inj1
(
Inj1
(
x6
0
)
)
)
)
(
setsum
(
Inj1
(
setsum
0
(
Inj1
0
)
)
)
(
setsum
(
x6
x7
)
(
Inj1
(
Inj0
0
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
(
(
ι → ι
)
→
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x6 :
ι →
ι →
ι →
ι → ι
.
∀ x7 :
ι → ι
.
x0
(
λ x8 .
setsum
(
setsum
(
setsum
x8
(
x6
0
0
0
0
)
)
x8
)
(
setsum
0
0
)
)
(
setsum
(
x5
(
λ x8 :
ι → ι
.
λ x9 x10 .
setsum
x9
(
setsum
0
0
)
)
(
λ x8 .
x8
)
)
(
setsum
(
x6
(
setsum
0
0
)
(
setsum
0
0
)
(
Inj1
0
)
(
x7
0
)
)
(
setsum
0
(
x6
0
0
0
0
)
)
)
)
⟶
False
)
⟶
False
)
Known
91710..
:
not
(
∀ x0 :
(
ι → ι
)
→
(
ι → ι
)
→
ι → ο
.
∀ x1 :
(
ι → ι
)
→
(
ι → ι
)
→
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ο
.
∀ x2 :
(
ι → ι
)
→
(
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ο
.
∀ x3 :
(
(
ι →
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
)
→
(
(
ι →
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→ ο
.
(
∀ x4 .
∀ x5 :
(
ι → ι
)
→
ι → ι
.
∀ x6 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
∀ x7 .
x2
(
λ x8 .
x7
)
(
λ x8 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
x8
(
λ x9 :
ι → ι
.
λ x10 .
setsum
(
x8
(
λ x11 :
ι → ι
.
λ x12 .
setsum
0
0
)
(
λ x11 .
x8
(
λ x12 :
ι → ι
.
λ x13 .
0
)
(
λ x12 .
0
)
0
)
0
)
(
setsum
(
setsum
0
0
)
x10
)
)
(
λ x9 .
Inj1
0
)
0
)
⟶
x3
(
λ x8 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
setsum
(
Inj0
(
x6
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
0
)
)
)
(
Inj1
0
)
)
(
λ x8 :
ι →
(
ι → ι
)
→ ι
.
λ x9 x10 .
x8
x7
(
λ x11 .
setsum
(
x8
(
Inj0
0
)
(
λ x12 .
x11
)
)
(
Inj1
x11
)
)
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→
ι →
ι → ι
.
∀ x5 x6 x7 .
In
(
Inj1
x5
)
(
x4
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 :
ι → ι
.
Inj1
(
setsum
(
setsum
0
0
)
0
)
)
(
λ x8 x9 .
x9
)
0
(
setsum
0
x6
)
)
⟶
x3
(
λ x8 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
setsum
x6
x6
)
(
λ x8 :
ι →
(
ι → ι
)
→ ι
.
λ x9 x10 .
setsum
(
setsum
(
Inj1
(
Inj1
0
)
)
0
)
(
Inj0
(
Inj0
x7
)
)
)
⟶
x1
(
λ x8 .
setsum
0
0
)
(
λ x8 .
setsum
(
setsum
(
setsum
(
Inj0
0
)
(
Inj1
0
)
)
x5
)
x7
)
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
0
)
)
⟶
(
∀ x4 x5 x6 x7 .
In
(
setsum
(
Inj1
(
Inj0
(
Inj1
0
)
)
)
x5
)
(
Inj1
0
)
⟶
x2
(
λ x8 .
setsum
(
Inj1
0
)
(
Inj1
(
setsum
0
(
setsum
0
0
)
)
)
)
(
λ x8 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
Inj1
0
)
)
⟶
(
∀ x4 :
ι →
(
ι → ι
)
→ ι
.
∀ x5 x6 x7 .
x2
(
λ x8 .
Inj0
0
)
(
λ x8 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
0
)
⟶
x0
(
λ x8 .
x8
)
(
λ x8 .
0
)
(
setsum
(
Inj1
(
Inj1
x7
)
)
(
setsum
(
Inj0
(
Inj0
0
)
)
(
Inj1
(
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 :
ι →
ι → ι
.
∀ x5 :
(
ι →
ι →
ι → ι
)
→
(
ι →
ι → ι
)
→
ι → ι
.
∀ x6 .
∀ x7 :
ι → ι
.
x1
(
λ x8 .
Inj0
(
Inj0
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
)
(
λ x8 .
x8
)
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
Inj0
(
x9
0
)
)
)
⟶
(
∀ x4 .
∀ x5 x6 :
ι →
ι → ι
.
∀ x7 .
In
x7
(
setsum
x7
(
x5
(
x5
(
x6
0
0
)
(
setsum
0
0
)
)
(
x5
(
x6
0
0
)
0
)
)
)
⟶
x1
(
λ x8 .
x7
)
(
λ x8 .
0
)
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
x8
)
⟶
x3
(
λ x8 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
Inj1
(
Inj1
(
setsum
(
setsum
0
0
)
(
Inj0
0
)
)
)
)
(
λ x8 :
ι →
(
ι → ι
)
→ ι
.
λ x9 x10 .
setsum
x9
x7
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
.
∀ x5 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
ι →
ι → ι
)
→
ι → ι
.
∀ x6 :
ι →
ι → ι
.
∀ x7 :
(
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
x0
(
λ x8 .
Inj0
(
Inj1
0
)
)
(
λ x8 .
Inj0
(
x7
(
λ x9 .
setsum
0
(
Inj0
0
)
)
(
λ x9 :
ι → ι
.
Inj1
0
)
x8
0
)
)
(
Inj0
(
setsum
0
(
x4
(
λ x8 :
(
ι → ι
)
→ ι
.
Inj1
0
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
)
→
ι → ι
.
∀ x6 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
∀ x7 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
In
(
x7
(
λ x8 :
ι →
ι → ι
.
λ x9 :
ι → ι
.
x8
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
(
Inj1
(
x6
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
0
)
)
)
)
0
0
)
(
Inj1
(
x6
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
x6
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
setsum
0
0
)
)
)
)
⟶
x0
(
λ x8 .
0
)
(
λ x8 .
0
)
(
Inj0
0
)
⟶
x2
(
λ x8 .
setsum
0
(
setsum
(
Inj1
0
)
(
setsum
(
Inj0
0
)
(
Inj0
0
)
)
)
)
(
λ x8 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
x5
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
Inj1
(
setsum
(
setsum
0
0
)
0
)
)
(
x5
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
setsum
0
(
x10
0
)
)
(
setsum
(
Inj0
0
)
(
Inj0
0
)
)
)
)
)
⟶
False
)
Known
05d15..
:
not
(
∀ x0 :
(
(
ι →
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ο
.
∀ x1 :
(
(
ι → ι
)
→
ι →
ι →
(
ι → ι
)
→
ι → ι
)
→
(
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
)
→
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ο
.
∀ x2 :
(
ι → ι
)
→
(
ι → ι
)
→ ο
.
∀ x3 :
(
ι → ι
)
→
ι → ο
.
(
∀ x4 x5 x6 x7 .
In
(
setsum
(
Inj0
0
)
0
)
(
Inj0
(
Inj1
x5
)
)
⟶
x3
(
λ x8 .
setsum
x8
(
setsum
(
setsum
(
Inj0
0
)
0
)
(
setsum
0
x5
)
)
)
x4
)
⟶
(
∀ x4 :
(
(
ι →
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x5 :
ι → ι
.
∀ x6 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→ ι
.
∀ x7 :
ι → ι
.
x3
(
λ x8 .
setsum
(
Inj0
(
Inj1
(
x6
(
λ x9 :
ι →
ι → ι
.
λ x10 :
ι → ι
.
λ x11 .
0
)
0
(
λ x9 .
0
)
)
)
)
(
Inj1
(
setsum
(
setsum
0
0
)
(
Inj0
0
)
)
)
)
(
x5
0
)
⟶
x1
(
λ x8 :
ι → ι
.
λ x9 x10 .
λ x11 :
ι → ι
.
λ x12 .
Inj0
x9
)
(
λ x8 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
x9
(
λ x11 .
setsum
0
(
Inj1
0
)
)
)
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
λ x9 :
ι → ι
.
Inj1
(
setsum
(
setsum
(
x6
(
λ x10 :
ι →
ι → ι
.
λ x11 :
ι → ι
.
λ x12 .
0
)
0
(
λ x10 .
0
)
)
(
setsum
0
0
)
)
0
)
)
)
⟶
(
∀ x4 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
∀ x5 x6 x7 .
In
(
Inj1
(
setsum
0
(
Inj1
(
x4
0
0
(
λ x8 .
0
)
0
)
)
)
)
(
setsum
(
setsum
(
Inj0
(
Inj1
0
)
)
0
)
x5
)
⟶
x1
(
λ x8 :
ι → ι
.
λ x9 x10 .
λ x11 :
ι → ι
.
λ x12 .
Inj1
0
)
(
λ x8 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
Inj1
(
x10
(
setsum
(
x10
0
)
(
setsum
0
0
)
)
)
)
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
λ x9 :
ι → ι
.
0
)
⟶
x2
(
λ x8 .
Inj1
x7
)
(
setsum
(
Inj1
(
Inj0
(
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→ ι
.
∀ x5 x6 .
∀ x7 :
(
ι →
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
In
(
x7
(
λ x8 x9 .
0
)
(
λ x8 x9 .
Inj1
(
setsum
(
x7
(
λ x10 x11 .
0
)
(
λ x10 x11 .
0
)
)
(
setsum
0
0
)
)
)
)
(
Inj0
0
)
⟶
x2
(
λ x8 .
0
)
(
λ x8 .
0
)
⟶
x0
(
λ x8 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
Inj1
(
Inj1
0
)
)
(
λ x8 .
λ x9 x10 :
ι → ι
.
λ x11 .
setsum
(
Inj1
(
Inj1
(
setsum
0
0
)
)
)
(
x9
0
)
)
(
λ x8 .
0
)
(
Inj1
(
x4
(
λ x8 .
x8
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x6 :
ι → ι
.
∀ x7 .
x2
(
λ x8 .
0
)
(
λ x8 .
0
)
⟶
x1
(
λ x8 :
ι → ι
.
λ x9 x10 .
λ x11 :
ι → ι
.
λ x12 .
0
)
(
λ x8 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
0
)
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
λ x9 :
ι → ι
.
setsum
(
setsum
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
(
Inj0
0
)
)
(
Inj1
0
)
)
)
⟶
(
∀ x4 .
∀ x5 :
(
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
∀ x6 :
ι → ι
.
∀ x7 :
(
(
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
x1
(
λ x8 :
ι → ι
.
λ x9 x10 .
λ x11 :
ι → ι
.
λ x12 .
x11
(
Inj1
(
Inj0
x10
)
)
)
(
λ x8 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
0
)
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
λ x9 :
ι → ι
.
0
)
⟶
x3
(
λ x8 .
0
)
(
Inj0
(
Inj1
(
x5
(
λ x8 x9 .
0
)
(
λ x8 :
ι → ι
.
setsum
0
0
)
(
λ x8 .
0
)
)
)
)
)
⟶
(
∀ x4 :
ι →
ι → ι
.
∀ x5 :
ι →
(
ι → ι
)
→ ι
.
∀ x6 :
(
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→ ι
.
∀ x7 :
ι → ι
.
In
(
Inj0
(
Inj1
0
)
)
(
x5
(
Inj0
(
setsum
0
0
)
)
(
λ x8 .
0
)
)
⟶
x0
(
λ x8 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x8 .
λ x9 x10 :
ι → ι
.
λ x11 .
setsum
(
Inj0
(
x10
(
setsum
0
0
)
)
)
(
Inj0
x11
)
)
(
λ x8 .
x6
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 .
setsum
(
setsum
(
x7
0
)
(
Inj0
0
)
)
0
)
0
(
λ x9 .
setsum
(
setsum
(
Inj1
0
)
(
setsum
0
0
)
)
(
setsum
x9
(
x6
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 .
0
)
0
(
λ x10 .
0
)
)
)
)
)
(
setsum
(
setsum
0
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
(
Inj0
0
)
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
∀ x5 x6 .
∀ x7 :
(
(
ι →
ι → ι
)
→ ι
)
→ ι
.
x0
(
λ x8 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
Inj1
x6
)
(
λ x8 .
λ x9 x10 :
ι → ι
.
λ x11 .
0
)
(
λ x8 .
Inj0
(
setsum
(
Inj1
(
setsum
0
0
)
)
0
)
)
(
Inj0
x5
)
⟶
x2
(
λ x8 .
x6
)
(
λ x8 .
x7
(
λ x9 :
ι →
ι → ι
.
setsum
(
setsum
x6
(
setsum
0
0
)
)
0
)
)
)
⟶
False
)
Known
6993e..
:
not
(
∀ x0 :
(
(
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
)
→
ι →
ι →
(
(
ι → ι
)
→ ι
)
→
ι → ο
.
∀ x1 :
(
ι →
ι →
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ο
.
∀ x2 :
(
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→
ι → ο
.
∀ x3 :
(
(
ι →
ι → ι
)
→
ι → ι
)
→
ι →
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ο
.
(
∀ x4 x5 x6 .
∀ x7 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
.
In
(
Inj0
0
)
x6
⟶
x0
(
λ x8 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
setsum
(
setsum
(
setsum
(
x7
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 .
0
)
)
(
x7
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 .
0
)
)
)
(
setsum
0
0
)
)
x5
)
(
setsum
(
Inj1
0
)
(
x7
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
Inj1
(
Inj1
0
)
)
)
)
(
Inj1
0
)
(
λ x8 :
ι → ι
.
x7
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 .
0
)
)
(
Inj0
x5
)
⟶
x3
(
λ x8 :
ι →
ι → ι
.
λ x9 .
x8
(
Inj0
0
)
(
Inj0
0
)
)
x5
(
λ x8 :
(
ι → ι
)
→ ι
.
0
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 :
(
ι → ι
)
→ ι
.
∀ x6 x7 .
x3
(
λ x8 :
ι →
ι → ι
.
λ x9 .
Inj0
x6
)
(
setsum
(
setsum
(
setsum
(
Inj0
0
)
(
setsum
0
0
)
)
0
)
(
setsum
0
(
x5
(
λ x8 .
setsum
0
0
)
)
)
)
(
λ x8 :
(
ι → ι
)
→ ι
.
x8
(
λ x9 .
Inj1
(
setsum
0
(
setsum
0
0
)
)
)
)
⟶
x1
(
λ x8 x9 .
λ x10 :
ι → ι
.
x7
)
(
λ x8 .
setsum
(
Inj0
(
setsum
(
Inj0
0
)
0
)
)
x7
)
)
⟶
(
∀ x4 :
(
ι →
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x5 :
ι → ι
.
∀ x6 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x7 :
ι →
(
ι → ι
)
→ ι
.
x2
(
λ x8 x9 .
Inj1
0
)
(
λ x8 :
ι → ι
.
setsum
0
(
x7
(
Inj1
(
setsum
0
0
)
)
(
λ x9 .
Inj1
(
setsum
0
0
)
)
)
)
(
λ x8 :
ι →
ι → ι
.
λ x9 x10 .
x7
(
Inj0
x9
)
(
λ x11 .
x8
(
setsum
(
Inj0
0
)
(
Inj1
0
)
)
x10
)
)
0
⟶
x2
(
λ x8 x9 .
0
)
(
λ x8 :
ι → ι
.
Inj0
0
)
(
λ x8 :
ι →
ι → ι
.
λ x9 x10 .
Inj1
(
Inj0
(
Inj0
(
Inj1
0
)
)
)
)
(
x7
(
x4
(
λ x8 x9 .
setsum
0
(
Inj0
0
)
)
(
λ x8 :
ι → ι
.
λ x9 .
x6
0
(
λ x10 :
ι → ι
.
x7
0
(
λ x11 .
0
)
)
)
(
λ x8 .
Inj1
0
)
)
(
λ x8 .
Inj1
(
Inj0
(
Inj1
0
)
)
)
)
)
⟶
(
∀ x4 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
∀ x5 :
ι → ι
.
∀ x6 :
ι →
ι →
ι →
ι → ι
.
∀ x7 :
ι →
(
ι →
ι → ι
)
→
ι →
ι → ι
.
x2
(
λ x8 x9 .
setsum
x9
x9
)
(
λ x8 :
ι → ι
.
0
)
(
λ x8 :
ι →
ι → ι
.
λ x9 x10 .
Inj0
(
Inj0
(
setsum
0
(
x7
0
(
λ x11 x12 .
0
)
0
0
)
)
)
)
(
Inj0
(
Inj0
(
Inj1
(
setsum
0
0
)
)
)
)
⟶
x1
(
λ x8 x9 .
λ x10 :
ι → ι
.
Inj1
x8
)
(
λ x8 .
setsum
(
Inj0
(
x5
(
Inj0
0
)
)
)
(
x6
0
x8
x8
(
Inj0
(
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x6 x7 .
x2
(
λ x8 x9 .
setsum
0
(
Inj1
0
)
)
(
λ x8 :
ι → ι
.
x6
)
(
λ x8 :
ι →
ι → ι
.
λ x9 x10 .
x9
)
0
⟶
x1
(
λ x8 x9 .
λ x10 :
ι → ι
.
setsum
(
Inj0
(
setsum
(
x10
0
)
(
setsum
0
0
)
)
)
(
setsum
(
setsum
x7
(
Inj1
0
)
)
0
)
)
(
λ x8 .
0
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→ ι
.
∀ x5 .
∀ x6 :
ι → ι
.
∀ x7 :
ι →
(
ι → ι
)
→ ι
.
In
(
Inj1
0
)
(
setsum
0
(
x4
(
λ x8 .
x8
)
)
)
⟶
x1
(
λ x8 x9 .
λ x10 :
ι → ι
.
x7
(
Inj1
0
)
(
λ x11 .
0
)
)
(
λ x8 .
0
)
⟶
x1
(
λ x8 x9 .
λ x10 :
ι → ι
.
x7
(
setsum
(
setsum
x9
0
)
x9
)
(
λ x11 .
setsum
0
x9
)
)
(
setsum
(
setsum
0
(
Inj1
(
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
(
(
ι → ι
)
→ ι
)
→ ι
.
In
(
Inj0
0
)
(
setsum
0
(
setsum
(
setsum
(
Inj0
0
)
(
x7
(
λ x8 :
ι → ι
.
0
)
)
)
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
)
⟶
x0
(
λ x8 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
x8
(
λ x9 :
ι →
ι → ι
.
λ x10 :
ι → ι
.
λ x11 .
0
)
(
λ x9 :
ι → ι
.
λ x10 .
Inj0
(
Inj1
(
setsum
0
0
)
)
)
)
(
setsum
0
(
Inj1
(
setsum
0
(
Inj0
0
)
)
)
)
(
x7
(
λ x8 :
ι → ι
.
Inj1
(
Inj1
x6
)
)
)
(
λ x8 :
ι → ι
.
Inj0
(
x8
x5
)
)
0
⟶
x0
(
λ x8 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
(
Inj0
(
setsum
x5
x6
)
)
0
(
λ x8 :
ι → ι
.
setsum
(
Inj1
(
setsum
0
0
)
)
(
Inj0
x6
)
)
0
)
⟶
(
∀ x4 :
(
ι →
ι → ι
)
→ ι
.
∀ x5 x6 .
∀ x7 :
ι →
ι → ι
.
In
(
setsum
0
0
)
(
Inj1
(
Inj1
(
Inj0
(
Inj0
0
)
)
)
)
⟶
x0
(
λ x8 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
Inj0
0
)
(
Inj1
(
setsum
0
(
Inj1
(
Inj0
0
)
)
)
)
x5
(
λ x8 :
ι → ι
.
setsum
x6
x5
)
(
setsum
(
setsum
(
setsum
0
0
)
0
)
0
)
⟶
x3
(
λ x8 :
ι →
ι → ι
.
λ x9 .
Inj0
0
)
0
(
λ x8 :
(
ι → ι
)
→ ι
.
setsum
0
(
setsum
(
x7
(
x7
0
0
)
(
setsum
0
0
)
)
(
x7
(
setsum
0
0
)
(
setsum
0
0
)
)
)
)
)
⟶
False
)
Known
30bb5..
:
not
(
∀ x0 :
(
(
ι →
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι →
ι → ι
)
→
(
(
ι →
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ο
.
∀ x1 :
(
ι → ι
)
→
(
(
ι →
ι →
ι → ι
)
→ ι
)
→ ο
.
∀ x2 :
(
(
ι →
ι → ι
)
→
ι →
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ο
.
∀ x3 :
(
ι →
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
ι →
ι → ο
.
(
∀ x4 x5 x6 .
∀ x7 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
.
x3
(
λ x8 .
λ x9 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x10 .
setsum
(
setsum
(
setsum
(
Inj1
0
)
(
Inj0
0
)
)
(
x9
(
λ x11 x12 .
x10
)
(
λ x11 .
Inj1
0
)
)
)
(
x7
(
λ x11 :
(
ι → ι
)
→ ι
.
x9
(
λ x12 x13 .
Inj0
0
)
(
λ x12 .
0
)
)
)
)
(
setsum
(
setsum
(
Inj1
(
setsum
0
0
)
)
0
)
(
Inj1
(
Inj1
(
setsum
0
0
)
)
)
)
(
setsum
(
setsum
(
Inj0
(
setsum
0
0
)
)
(
Inj1
0
)
)
(
Inj0
(
Inj0
(
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x6 x7 .
x3
(
λ x8 .
λ x9 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x10 .
setsum
0
(
setsum
(
setsum
x8
(
Inj0
0
)
)
(
Inj1
(
setsum
0
0
)
)
)
)
(
Inj1
x7
)
(
x5
x4
(
λ x8 x9 .
x7
)
(
λ x8 .
setsum
x6
0
)
(
x5
(
x5
(
setsum
0
0
)
(
λ x8 x9 .
Inj1
0
)
(
λ x8 .
Inj1
0
)
(
Inj0
0
)
)
(
λ x8 x9 .
Inj1
(
setsum
0
0
)
)
(
λ x8 .
setsum
0
0
)
0
)
)
⟶
x1
(
λ x8 .
Inj1
0
)
(
λ x8 :
ι →
ι →
ι → ι
.
x5
(
Inj0
(
Inj0
0
)
)
(
λ x9 x10 .
setsum
0
0
)
(
λ x9 .
x6
)
(
setsum
(
x8
0
x7
(
Inj0
0
)
)
(
x5
0
(
λ x9 x10 .
Inj1
0
)
(
λ x9 .
Inj1
0
)
(
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
(
ι → ι
)
→ ι
.
∀ x6 :
ι → ι
.
∀ x7 .
x2
(
λ x8 :
ι →
ι → ι
.
λ x9 x10 x11 .
0
)
(
λ x8 .
x7
)
(
x6
(
setsum
(
Inj0
0
)
(
setsum
(
setsum
0
0
)
0
)
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 .
∀ x6 :
ι → ι
.
∀ x7 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
In
(
Inj0
(
Inj1
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
)
(
setsum
0
0
)
⟶
x2
(
λ x8 :
ι →
ι → ι
.
λ x9 x10 x11 .
Inj0
(
setsum
(
Inj0
(
Inj0
0
)
)
0
)
)
(
λ x8 .
x7
(
λ x9 :
(
ι → ι
)
→ ι
.
Inj1
(
setsum
0
0
)
)
(
λ x9 x10 .
Inj1
x9
)
)
(
setsum
x5
0
)
⟶
x1
(
λ x8 .
setsum
0
(
x7
(
λ x9 :
(
ι → ι
)
→ ι
.
x6
(
setsum
0
0
)
)
(
λ x9 x10 .
Inj1
(
setsum
0
0
)
)
)
)
(
λ x8 :
ι →
ι →
ι → ι
.
Inj0
(
Inj0
(
Inj0
(
Inj0
0
)
)
)
)
)
⟶
(
∀ x4 :
(
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
∀ x5 x6 x7 .
In
(
setsum
(
setsum
(
x4
(
λ x8 x9 :
ι → ι
.
λ x10 .
0
)
x5
)
(
setsum
(
Inj0
0
)
x6
)
)
0
)
(
Inj0
(
setsum
(
Inj0
(
Inj1
0
)
)
x5
)
)
⟶
x3
(
λ x8 .
λ x9 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x10 .
0
)
0
x7
⟶
x1
(
λ x8 .
0
)
(
λ x8 :
ι →
ι →
ι → ι
.
0
)
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 .
∀ x7 :
(
ι → ι
)
→
ι →
ι → ι
.
x1
(
λ x8 .
0
)
(
λ x8 :
ι →
ι →
ι → ι
.
x6
)
⟶
x0
(
λ x8 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
x7
(
λ x9 .
Inj0
(
Inj1
0
)
)
(
x8
(
Inj1
(
setsum
0
0
)
)
(
λ x9 :
ι → ι
.
λ x10 .
0
)
(
x8
(
setsum
0
0
)
(
λ x9 :
ι → ι
.
λ x10 .
x9
0
)
0
)
)
(
x7
(
λ x9 .
setsum
(
setsum
0
0
)
(
Inj1
0
)
)
(
Inj0
(
setsum
0
0
)
)
x6
)
)
(
λ x8 x9 .
Inj0
)
(
λ x8 :
ι →
ι → ι
.
Inj0
(
setsum
(
setsum
(
Inj1
0
)
(
setsum
0
0
)
)
(
setsum
(
Inj1
0
)
0
)
)
)
(
λ x8 :
ι → ι
.
x6
)
(
λ x8 .
x6
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
ι → ι
.
∀ x6 :
ι → ι
.
∀ x7 .
In
(
setsum
0
(
setsum
(
setsum
(
Inj0
0
)
(
setsum
0
0
)
)
0
)
)
(
Inj1
(
Inj1
x7
)
)
⟶
x0
(
λ x8 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
0
)
(
λ x8 x9 x10 .
Inj0
(
Inj1
x8
)
)
(
λ x8 :
ι →
ι → ι
.
0
)
(
λ x8 :
ι → ι
.
x6
(
setsum
0
(
Inj1
(
x8
0
)
)
)
)
(
λ x8 .
Inj1
(
Inj1
(
Inj0
(
x5
0
0
)
)
)
)
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
ι →
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
x0
(
λ x8 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
x8
(
x8
(
setsum
(
Inj1
0
)
(
x8
0
(
λ x9 :
ι → ι
.
λ x10 .
0
)
0
)
)
(
λ x9 :
ι → ι
.
λ x10 .
Inj0
(
x8
0
(
λ x11 :
ι → ι
.
λ x12 .
0
)
0
)
)
(
setsum
0
0
)
)
(
λ x9 :
ι → ι
.
λ x10 .
0
)
(
setsum
(
Inj1
x6
)
x6
)
)
(
λ x8 x9 x10 .
Inj1
(
setsum
(
Inj0
(
Inj1
0
)
)
x9
)
)
(
λ x8 :
ι →
ι → ι
.
0
)
(
λ x8 :
ι → ι
.
x8
x6
)
(
λ x8 .
setsum
x8
(
Inj1
(
setsum
x5
(
setsum
0
0
)
)
)
)
⟶
x0
(
λ x8 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
x8
0
(
λ x9 :
ι → ι
.
λ x10 .
Inj0
(
setsum
0
0
)
)
(
setsum
x6
(
Inj1
(
Inj1
0
)
)
)
)
(
λ x8 x9 x10 .
0
)
(
λ x8 :
ι →
ι → ι
.
Inj1
(
setsum
x5
0
)
)
(
λ x8 :
ι → ι
.
0
)
(
λ x8 .
setsum
0
0
)
)
⟶
False
)
Known
6c860..
:
not
(
∀ x0 :
(
ι →
ι → ι
)
→
ι → ο
.
∀ x1 :
(
ι → ι
)
→
ι → ο
.
∀ x2 :
(
ι →
ι → ι
)
→
(
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
)
→
ι → ο
.
∀ x3 :
(
ι →
ι →
ι → ι
)
→
ι → ο
.
(
∀ x4 :
ι →
ι → ι
.
∀ x5 :
ι → ι
.
∀ x6 :
(
ι → ι
)
→
ι →
(
ι → ι
)
→ ι
.
∀ x7 .
x2
(
λ x8 x9 .
setsum
0
(
setsum
(
setsum
x8
(
x6
(
λ x10 .
0
)
0
(
λ x10 .
0
)
)
)
x7
)
)
(
λ x8 :
ι → ι
.
λ x9 :
ι →
ι → ι
.
x6
(
λ x10 .
Inj0
(
setsum
0
0
)
)
(
setsum
(
Inj1
0
)
(
setsum
(
Inj1
0
)
(
x8
0
)
)
)
(
λ x10 .
0
)
)
x7
⟶
x3
(
λ x8 x9 x10 .
x9
)
0
)
⟶
(
∀ x4 x5 .
∀ x6 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x7 .
In
(
Inj0
0
)
(
Inj1
(
setsum
0
(
setsum
0
(
setsum
0
0
)
)
)
)
⟶
x3
(
λ x8 x9 x10 .
Inj1
(
Inj0
0
)
)
(
Inj1
0
)
⟶
x1
(
λ x8 .
0
)
(
Inj1
(
Inj0
(
Inj0
(
Inj0
0
)
)
)
)
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
ι → ι
.
In
(
Inj0
0
)
(
Inj0
(
Inj0
(
Inj1
(
Inj0
0
)
)
)
)
⟶
x2
(
λ x8 x9 .
0
)
(
λ x8 :
ι → ι
.
λ x9 :
ι →
ι → ι
.
setsum
(
Inj1
(
setsum
(
Inj0
0
)
0
)
)
x6
)
0
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 :
(
ι →
ι → ι
)
→
ι → ι
.
∀ x6 .
∀ x7 :
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
In
(
Inj0
(
setsum
0
(
setsum
0
(
Inj0
0
)
)
)
)
x6
⟶
x2
(
λ x8 x9 .
setsum
0
x6
)
(
λ x8 :
ι → ι
.
λ x9 :
ι →
ι → ι
.
Inj0
(
x9
0
0
)
)
(
setsum
(
x5
(
λ x8 x9 .
Inj1
0
)
(
x5
(
λ x8 x9 .
x9
)
(
setsum
0
0
)
)
)
0
)
⟶
x0
(
λ x8 x9 .
setsum
(
setsum
x9
(
setsum
(
setsum
0
0
)
0
)
)
x6
)
(
setsum
(
setsum
(
x7
(
Inj1
0
)
(
λ x8 x9 .
setsum
0
0
)
(
λ x8 .
setsum
0
0
)
0
)
(
setsum
(
Inj0
0
)
(
setsum
0
0
)
)
)
(
setsum
(
Inj1
(
Inj1
0
)
)
(
setsum
(
x4
0
)
(
Inj0
0
)
)
)
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→
ι →
ι →
ι → ι
.
∀ x5 :
ι →
(
ι → ι
)
→ ι
.
∀ x6 x7 .
x1
(
λ x8 .
0
)
(
Inj1
0
)
)
⟶
(
∀ x4 x5 x6 x7 .
x1
(
λ x8 .
0
)
x5
⟶
x1
(
λ x8 .
x6
)
0
)
⟶
(
∀ x4 x5 x6 x7 .
In
(
Inj1
(
Inj0
(
Inj1
0
)
)
)
(
Inj1
(
Inj1
0
)
)
⟶
x0
(
λ x8 x9 .
x7
)
(
setsum
0
0
)
)
⟶
(
∀ x4 .
∀ x5 x6 :
ι → ι
.
∀ x7 .
x0
(
λ x8 x9 .
0
)
(
x5
(
Inj0
(
Inj0
0
)
)
)
⟶
x3
(
λ x8 x9 x10 .
0
)
0
)
⟶
False
)
Known
1b96e..
:
not
(
∀ x0 :
(
(
(
(
ι → ι
)
→
ι →
ι → ι
)
→ ι
)
→
(
ι →
ι →
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ο
.
∀ x1 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ο
.
∀ x2 :
(
ι → ι
)
→
ι →
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ο
.
∀ x3 :
(
ι → ι
)
→
(
(
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
)
→
ι → ι
)
→ ο
.
(
∀ x4 :
ι →
ι →
(
ι → ι
)
→ ι
.
∀ x5 .
∀ x6 :
ι → ι
.
∀ x7 .
x0
(
λ x8 :
(
(
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
λ x9 :
ι →
ι →
ι → ι
.
setsum
0
(
x9
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
(
Inj1
0
)
0
)
)
(
λ x8 .
x7
)
⟶
x3
(
λ x8 .
Inj0
(
x6
(
setsum
(
Inj0
0
)
(
x6
0
)
)
)
)
(
λ x8 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
λ x9 .
x7
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→ ι
.
∀ x5 :
ι →
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
∀ x6 .
∀ x7 :
(
ι → ι
)
→
ι → ι
.
x3
(
λ x8 .
setsum
(
Inj0
0
)
(
Inj0
0
)
)
(
λ x8 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
λ x9 .
0
)
⟶
x1
(
λ x8 .
λ x9 :
ι → ι
.
0
)
(
Inj1
0
)
)
⟶
(
∀ x4 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
∀ x5 :
(
ι →
(
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x6 x7 .
In
(
Inj1
0
)
(
setsum
x7
(
Inj0
(
setsum
0
(
x4
(
λ x8 :
ι →
ι → ι
.
λ x9 :
ι → ι
.
0
)
)
)
)
)
⟶
x2
(
λ x8 .
setsum
(
Inj1
0
)
(
Inj0
0
)
)
(
Inj1
(
setsum
0
0
)
)
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
setsum
(
setsum
0
(
Inj1
(
Inj0
0
)
)
)
(
setsum
x6
0
)
)
⟶
x2
(
λ x8 .
0
)
x7
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
0
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
∀ x6 x7 .
In
x7
(
Inj1
(
setsum
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
(
x5
(
setsum
0
0
)
(
setsum
0
0
)
(
λ x8 .
0
)
0
)
)
)
⟶
x2
(
λ x8 .
Inj1
x6
)
(
x5
(
Inj0
(
setsum
x6
0
)
)
x7
(
λ x8 .
x7
)
x4
)
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
Inj1
x7
)
⟶
x0
(
λ x8 :
(
(
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
λ x9 :
ι →
ι →
ι → ι
.
0
)
(
λ x8 .
x8
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
∀ x5 :
(
ι → ι
)
→ ι
.
∀ x6 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→ ι
.
∀ x7 :
ι → ι
.
In
(
setsum
(
setsum
(
x6
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 .
setsum
0
0
)
(
setsum
0
0
)
(
λ x8 .
setsum
0
0
)
)
(
Inj0
(
setsum
0
0
)
)
)
(
setsum
0
(
Inj0
(
Inj1
0
)
)
)
)
(
x6
(
λ x8 :
(
ι → ι
)
→ ι
.
x7
)
0
(
λ x8 .
0
)
)
⟶
x1
(
λ x8 .
λ x9 :
ι → ι
.
x9
0
)
(
Inj1
(
setsum
(
x7
(
Inj0
0
)
)
(
x7
(
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
(
(
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
∀ x6 x7 .
In
(
setsum
x4
x7
)
(
Inj1
(
setsum
(
setsum
(
setsum
0
0
)
0
)
x4
)
)
⟶
x1
(
λ x8 .
λ x9 :
ι → ι
.
0
)
0
⟶
x3
(
λ x8 .
x7
)
(
λ x8 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
λ x9 .
setsum
0
x6
)
)
⟶
(
∀ x4 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x5 .
∀ x6 :
ι →
ι →
ι →
ι → ι
.
∀ x7 .
x0
(
λ x8 :
(
(
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
λ x9 :
ι →
ι →
ι → ι
.
0
)
(
λ x8 .
0
)
⟶
x0
(
λ x8 :
(
(
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
λ x9 :
ι →
ι →
ι → ι
.
Inj0
(
setsum
x7
x7
)
)
(
λ x8 .
Inj1
(
Inj1
0
)
)
)
⟶
(
∀ x4 x5 x6 :
ι → ι
.
∀ x7 .
x0
(
λ x8 :
(
(
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
λ x9 :
ι →
ι →
ι → ι
.
x7
)
(
λ x8 .
Inj1
0
)
⟶
In
x7
(
x4
(
setsum
0
(
x4
(
Inj0
0
)
)
)
)
)
⟶
False
)
Known
c13a6..
:
not
(
∀ x0 :
(
ι →
(
(
ι →
ι → ι
)
→ ι
)
→ ι
)
→
(
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→ ι
)
→ ο
.
∀ x1 :
(
ι →
ι → ι
)
→
(
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι → ι
)
→
(
ι → ι
)
→
(
ι → ι
)
→
ι → ο
.
∀ x2 :
(
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
)
→
ι →
(
ι → ι
)
→
(
ι → ι
)
→ ο
.
∀ x3 :
(
(
(
ι →
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→
ι → ο
.
(
∀ x4 x5 .
∀ x6 :
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x7 :
ι → ι
.
In
(
x7
0
)
x4
⟶
x0
(
λ x8 .
λ x9 :
(
ι →
ι → ι
)
→ ι
.
Inj1
(
x6
(
λ x10 .
Inj0
0
)
(
λ x10 .
x10
)
)
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
0
)
⟶
x3
(
λ x8 :
(
ι →
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x9 .
λ x10 :
ι →
ι → ι
.
λ x11 x12 .
Inj1
0
)
0
)
⟶
(
∀ x4 .
∀ x5 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x6 .
∀ x7 :
ι → ι
.
In
(
setsum
0
(
Inj1
x6
)
)
(
Inj1
(
Inj1
(
x5
(
Inj1
0
)
(
λ x8 :
ι → ι
.
λ x9 .
0
)
)
)
)
⟶
x3
(
λ x8 :
(
ι →
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x9 .
λ x10 :
ι →
ι → ι
.
λ x11 x12 .
Inj1
0
)
x4
⟶
x2
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
setsum
(
setsum
(
setsum
(
setsum
0
0
)
0
)
(
setsum
(
setsum
0
0
)
(
Inj0
0
)
)
)
0
)
0
(
λ x8 .
0
)
(
λ x8 .
setsum
(
Inj0
(
Inj1
(
x5
0
(
λ x9 :
ι → ι
.
λ x10 .
0
)
)
)
)
0
)
)
⟶
(
∀ x4 .
∀ x5 x6 :
ι → ι
.
∀ x7 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
.
x0
(
λ x8 .
λ x9 :
(
ι →
ι → ι
)
→ ι
.
setsum
0
0
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
x7
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 .
setsum
(
setsum
(
setsum
0
0
)
(
Inj0
0
)
)
(
setsum
(
Inj1
0
)
(
setsum
0
0
)
)
)
)
⟶
x2
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
x6
0
)
0
(
λ x8 .
0
)
(
λ x8 .
0
)
)
⟶
(
∀ x4 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
∀ x5 :
(
ι → ι
)
→ ι
.
∀ x6 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x7 .
x2
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
x8
(
λ x9 :
ι → ι
.
x7
)
)
0
(
λ x8 .
Inj0
(
x6
(
λ x9 .
setsum
x8
(
Inj0
0
)
)
(
λ x9 :
ι → ι
.
λ x10 .
setsum
x7
(
setsum
0
0
)
)
(
λ x9 .
0
)
0
)
)
(
λ x8 .
setsum
x8
(
Inj0
0
)
)
⟶
False
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 :
ι →
ι → ι
.
∀ x6 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι → ι
)
→
ι →
ι → ι
.
∀ x7 :
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
x2
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
Inj0
(
setsum
(
x8
(
λ x9 :
ι → ι
.
Inj1
0
)
)
0
)
)
0
(
λ x8 .
0
)
(
λ x8 .
Inj1
(
Inj0
(
setsum
0
(
setsum
0
0
)
)
)
)
⟶
x1
(
λ x8 x9 .
setsum
0
0
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 .
Inj1
(
setsum
(
setsum
(
x6
(
λ x10 :
(
ι → ι
)
→ ι
.
0
)
(
λ x10 .
0
)
0
0
)
(
setsum
0
0
)
)
(
setsum
0
(
x8
(
λ x10 :
ι → ι
.
0
)
)
)
)
)
(
λ x8 .
Inj0
(
setsum
(
x6
(
λ x9 :
(
ι → ι
)
→ ι
.
x9
(
λ x10 .
0
)
)
(
λ x9 .
0
)
0
0
)
(
x6
(
λ x9 :
(
ι → ι
)
→ ι
.
setsum
0
0
)
(
λ x9 .
x7
0
(
λ x10 x11 .
0
)
(
λ x10 .
0
)
0
)
(
x5
0
0
)
0
)
)
)
(
λ x8 .
setsum
(
Inj0
(
setsum
0
0
)
)
(
Inj1
0
)
)
(
Inj1
(
x5
(
x7
(
Inj0
0
)
(
λ x8 x9 .
setsum
0
0
)
(
λ x8 .
setsum
0
0
)
(
x5
0
0
)
)
(
Inj1
(
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 :
(
(
ι →
ι → ι
)
→ ι
)
→ ι
.
∀ x5 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x6 :
ι → ι
.
∀ x7 .
x1
(
λ x8 x9 .
0
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 .
Inj0
(
x6
0
)
)
(
λ x8 .
0
)
(
λ x8 .
x7
)
(
x6
0
)
⟶
x2
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
0
)
0
(
λ x8 .
Inj1
(
x5
x8
(
λ x9 :
ι → ι
.
0
)
)
)
(
λ x8 .
setsum
(
Inj0
x8
)
(
x6
0
)
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x5 x6 x7 .
In
(
Inj0
x7
)
(
Inj0
x5
)
⟶
x2
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
x5
)
x7
(
λ x8 .
Inj0
(
setsum
(
Inj1
(
setsum
0
0
)
)
0
)
)
(
λ x8 .
0
)
⟶
x0
(
λ x8 .
λ x9 :
(
ι →
ι → ι
)
→ ι
.
x9
(
λ x10 x11 .
x9
(
λ x12 x13 .
x10
)
)
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
Inj0
0
)
)
⟶
(
∀ x4 .
∀ x5 :
(
ι → ι
)
→ ι
.
∀ x6 .
∀ x7 :
(
(
ι → ι
)
→ ι
)
→ ι
.
In
(
Inj1
0
)
(
Inj1
(
setsum
0
0
)
)
⟶
x0
(
λ x8 .
λ x9 :
(
ι →
ι → ι
)
→ ι
.
Inj0
(
setsum
0
(
setsum
(
Inj0
0
)
(
x9
(
λ x10 x11 .
0
)
)
)
)
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
Inj1
0
)
⟶
x0
(
λ x8 .
λ x9 :
(
ι →
ι → ι
)
→ ι
.
Inj1
0
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
setsum
0
(
x5
(
λ x9 .
0
)
)
)
)
⟶
False
)
Known
29cb8..
:
not
(
∀ x0 :
(
(
ι →
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→
ι → ο
.
∀ x1 :
(
ι → ι
)
→
(
ι →
(
ι →
ι → ι
)
→ ι
)
→
(
(
ι →
ι → ι
)
→ ι
)
→
ι → ο
.
∀ x2 :
(
ι → ι
)
→
(
(
(
ι →
ι → ι
)
→ ι
)
→ ι
)
→
ι → ο
.
∀ x3 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι →
ι → ο
.
(
∀ x4 :
(
ι → ι
)
→ ι
.
∀ x5 :
ι → ι
.
∀ x6 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x7 :
(
ι → ι
)
→ ι
.
In
(
Inj1
0
)
(
Inj1
(
x7
(
λ x8 .
setsum
(
Inj0
0
)
(
Inj1
0
)
)
)
)
⟶
x1
(
λ x8 .
Inj1
0
)
(
λ x8 .
λ x9 :
ι →
ι → ι
.
setsum
(
setsum
(
setsum
(
Inj1
0
)
0
)
0
)
(
setsum
(
setsum
(
setsum
0
0
)
0
)
(
setsum
0
(
x9
0
0
)
)
)
)
(
λ x8 :
ι →
ι → ι
.
0
)
(
Inj0
(
Inj0
(
setsum
0
(
x5
0
)
)
)
)
⟶
x3
(
λ x8 .
λ x9 :
ι → ι
.
x6
(
λ x10 :
ι → ι
.
λ x11 .
x10
(
Inj0
(
x9
0
)
)
)
)
(
x6
(
λ x8 :
ι → ι
.
λ x9 .
x6
(
λ x10 :
ι → ι
.
λ x11 .
setsum
(
setsum
0
0
)
(
Inj1
0
)
)
)
)
(
setsum
(
Inj0
0
)
0
)
)
⟶
(
∀ x4 .
∀ x5 :
(
(
ι →
ι → ι
)
→ ι
)
→ ι
.
∀ x6 :
(
(
ι →
ι → ι
)
→ ι
)
→
ι → ι
.
∀ x7 .
x3
(
λ x8 .
λ x9 :
ι → ι
.
setsum
(
setsum
x8
(
setsum
(
Inj1
0
)
(
setsum
0
0
)
)
)
0
)
(
x5
(
λ x8 :
ι →
ι → ι
.
x6
(
λ x9 :
ι →
ι → ι
.
setsum
0
(
setsum
0
0
)
)
x7
)
)
(
x5
(
λ x8 :
ι →
ι → ι
.
Inj0
0
)
)
⟶
In
(
Inj0
(
setsum
(
setsum
0
0
)
(
Inj0
(
setsum
0
0
)
)
)
)
(
Inj0
0
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x5 x6 x7 .
In
(
setsum
(
setsum
0
(
setsum
(
x4
(
λ x8 .
0
)
(
λ x8 :
ι → ι
.
0
)
)
x6
)
)
(
setsum
(
x4
(
λ x8 .
Inj1
0
)
(
λ x8 :
ι → ι
.
setsum
0
0
)
)
0
)
)
(
Inj1
(
Inj1
(
setsum
(
Inj1
0
)
0
)
)
)
⟶
x3
(
λ x8 .
λ x9 :
ι → ι
.
0
)
(
Inj0
(
setsum
x5
x5
)
)
0
⟶
x2
(
λ x8 .
0
)
(
λ x8 :
(
ι →
ι → ι
)
→ ι
.
Inj0
(
x8
(
λ x9 x10 .
0
)
)
)
x6
)
⟶
(
∀ x4 .
∀ x5 :
(
ι →
ι →
ι → ι
)
→
ι → ι
.
∀ x6 .
∀ x7 :
(
ι → ι
)
→
ι → ι
.
In
(
setsum
(
setsum
(
setsum
(
x7
(
λ x8 .
0
)
0
)
0
)
(
x7
(
λ x8 .
Inj1
0
)
(
setsum
0
0
)
)
)
x6
)
(
Inj0
x6
)
⟶
x2
(
λ x8 .
0
)
(
λ x8 :
(
ι →
ι → ι
)
→ ι
.
x5
(
λ x9 x10 x11 .
setsum
(
Inj1
x10
)
(
Inj0
(
Inj0
0
)
)
)
(
x5
(
λ x9 x10 x11 .
Inj0
0
)
0
)
)
(
Inj1
(
setsum
(
setsum
x6
(
Inj1
0
)
)
(
Inj0
(
Inj0
0
)
)
)
)
⟶
x0
(
λ x8 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
x7
(
λ x9 .
0
)
(
setsum
0
0
)
)
(
setsum
(
Inj0
0
)
x6
)
(
λ x8 .
setsum
(
Inj0
(
Inj0
(
Inj0
0
)
)
)
(
setsum
(
x5
(
λ x9 x10 x11 .
Inj1
0
)
(
setsum
0
0
)
)
(
setsum
0
0
)
)
)
(
Inj0
x6
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 :
ι →
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
∀ x6 .
∀ x7 :
(
(
ι → ι
)
→ ι
)
→ ι
.
x0
(
λ x8 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
setsum
(
setsum
(
x5
(
Inj1
0
)
(
λ x9 :
ι → ι
.
setsum
0
0
)
(
λ x9 .
setsum
0
0
)
)
(
x7
(
λ x9 :
ι → ι
.
setsum
0
0
)
)
)
(
setsum
(
setsum
0
(
setsum
0
0
)
)
(
setsum
(
x5
0
(
λ x9 :
ι → ι
.
0
)
(
λ x9 .
0
)
)
(
x8
0
0
(
λ x9 .
0
)
0
)
)
)
)
x6
(
λ x8 .
Inj1
(
Inj1
(
x5
(
x5
0
(
λ x9 :
ι → ι
.
0
)
(
λ x9 .
0
)
)
(
λ x9 :
ι → ι
.
x8
)
(
λ x9 .
Inj1
0
)
)
)
)
0
⟶
x1
(
λ x8 .
setsum
(
setsum
0
0
)
0
)
(
λ x8 .
λ x9 :
ι →
ι → ι
.
x9
x8
(
x9
(
Inj1
(
setsum
0
0
)
)
(
Inj1
(
x9
0
0
)
)
)
)
(
λ x8 :
ι →
ι → ι
.
x6
)
(
Inj1
0
)
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
x1
(
λ x8 .
x7
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
Inj1
(
x7
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
x10
(
λ x11 .
0
)
0
)
)
)
)
(
λ x8 .
λ x9 :
ι →
ι → ι
.
Inj0
0
)
(
λ x8 :
ι →
ι → ι
.
Inj1
(
setsum
0
x6
)
)
(
setsum
0
(
setsum
(
Inj1
0
)
0
)
)
⟶
In
(
setsum
0
(
setsum
0
(
Inj1
(
setsum
0
0
)
)
)
)
(
Inj0
(
setsum
(
Inj1
(
Inj1
0
)
)
(
Inj0
(
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 x7 .
x1
(
λ x8 .
0
)
(
λ x8 .
λ x9 :
ι →
ι → ι
.
x7
)
(
λ x8 :
ι →
ι → ι
.
x5
(
setsum
x7
(
setsum
(
Inj1
0
)
0
)
)
)
x7
⟶
x0
(
λ x8 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
Inj0
(
setsum
(
setsum
x6
x6
)
x7
)
)
0
(
λ x8 .
x8
)
(
Inj0
x7
)
)
⟶
(
∀ x4 x5 :
ι → ι
.
∀ x6 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x7 .
x0
(
λ x8 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
setsum
(
setsum
(
Inj1
(
x5
0
)
)
0
)
(
x6
(
λ x9 :
ι → ι
.
λ x10 .
Inj0
0
)
)
)
(
Inj1
x7
)
(
λ x8 .
x6
(
λ x9 :
ι → ι
.
λ x10 .
x9
0
)
)
x7
⟶
In
(
x6
(
λ x8 :
ι → ι
.
λ x9 .
setsum
(
Inj0
(
Inj0
0
)
)
(
Inj0
(
x8
0
)
)
)
)
(
Inj1
(
setsum
(
x4
(
setsum
0
0
)
)
(
setsum
(
x6
(
λ x8 :
ι → ι
.
λ x9 .
0
)
)
(
Inj0
0
)
)
)
)
)
⟶
False
)
Known
ee98d..
:
not
(
∀ x0 :
(
(
ι →
(
ι →
ι → ι
)
→ ι
)
→
(
ι →
ι →
ι → ι
)
→
ι → ι
)
→
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ο
.
∀ x1 :
(
(
ι →
(
ι →
ι → ι
)
→ ι
)
→
ι →
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι →
ι → ι
)
→ ο
.
∀ x2 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
(
(
ι → ι
)
→
ι →
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ο
.
∀ x3 :
(
ι → ι
)
→
(
ι →
ι →
ι →
ι → ι
)
→ ο
.
(
∀ x4 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
∀ x5 .
∀ x6 :
ι →
ι →
ι →
ι → ι
.
∀ x7 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
x3
(
λ x8 .
Inj0
(
setsum
(
Inj0
0
)
x5
)
)
(
λ x8 x9 x10 x11 .
x10
)
⟶
x3
(
λ x8 .
Inj1
(
Inj0
(
Inj1
(
Inj1
0
)
)
)
)
(
λ x8 x9 x10 x11 .
x11
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x5 :
ι → ι
.
∀ x6 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x7 :
(
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
In
(
x6
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
Inj0
(
Inj1
(
x9
0
)
)
)
)
(
x4
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 :
ι → ι
.
λ x10 .
0
)
)
⟶
x3
(
λ x8 .
Inj1
(
x6
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 .
0
)
)
)
(
λ x8 x9 x10 x11 .
0
)
⟶
x3
(
λ x8 .
0
)
(
λ x8 x9 x10 x11 .
x11
)
)
⟶
(
∀ x4 .
∀ x5 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
∀ x6 x7 .
x2
(
λ x8 :
ι →
ι → ι
.
λ x9 :
ι → ι
.
λ x10 .
Inj0
x7
)
(
λ x8 :
(
ι → ι
)
→
ι →
ι → ι
.
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 :
ι → ι
.
λ x11 .
setsum
(
Inj0
0
)
0
)
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
ι → ι
.
x2
(
λ x8 :
ι →
ι → ι
.
λ x9 :
ι → ι
.
λ x10 .
x9
(
setsum
0
0
)
)
(
λ x8 :
(
ι → ι
)
→
ι →
ι → ι
.
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 :
ι → ι
.
λ x11 .
x9
(
λ x12 .
x9
(
λ x13 .
0
)
(
x10
(
setsum
0
0
)
)
)
(
setsum
(
Inj0
(
x9
(
λ x12 .
0
)
0
)
)
(
setsum
(
setsum
0
0
)
x11
)
)
)
⟶
x3
(
λ x8 .
x7
0
)
(
λ x8 x9 x10 x11 .
x8
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 .
∀ x6 :
ι → ι
.
∀ x7 .
x0
(
λ x8 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x9 :
ι →
ι →
ι → ι
.
λ x10 .
0
)
(
λ x8 :
(
ι → ι
)
→ ι
.
setsum
(
setsum
x7
x5
)
(
setsum
(
Inj1
x5
)
0
)
)
⟶
x1
(
λ x8 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x9 .
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 .
0
)
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 x10 x11 .
setsum
0
(
Inj1
(
Inj1
(
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
ι →
ι → ι
.
∀ x6 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
∀ x7 :
ι →
ι → ι
.
x1
(
λ x8 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x9 .
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 .
0
)
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 x10 x11 .
setsum
(
setsum
(
Inj0
(
Inj0
0
)
)
(
setsum
(
Inj0
0
)
0
)
)
x10
)
⟶
False
)
⟶
(
∀ x4 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x5 x6 x7 .
x0
(
λ x8 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x9 :
ι →
ι →
ι → ι
.
λ x10 .
x9
(
Inj0
(
Inj0
x10
)
)
(
x9
x10
0
(
setsum
(
Inj0
0
)
(
setsum
0
0
)
)
)
x10
)
(
λ x8 :
(
ι → ι
)
→ ι
.
x6
)
⟶
x0
(
λ x8 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x9 :
ι →
ι →
ι → ι
.
λ x10 .
x9
0
(
setsum
(
setsum
(
Inj1
0
)
(
Inj1
0
)
)
0
)
(
setsum
(
setsum
0
0
)
(
Inj1
(
setsum
0
0
)
)
)
)
(
λ x8 :
(
ι → ι
)
→ ι
.
setsum
(
setsum
x5
(
Inj0
0
)
)
(
Inj1
x7
)
)
)
⟶
(
∀ x4 :
(
(
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
∀ x5 :
(
ι → ι
)
→
ι →
ι → ι
.
∀ x6 .
∀ x7 :
(
(
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
In
(
Inj1
(
x5
(
λ x8 .
0
)
(
setsum
(
setsum
0
0
)
x6
)
(
setsum
(
Inj1
0
)
(
x5
(
λ x8 .
0
)
0
0
)
)
)
)
(
Inj1
(
Inj0
0
)
)
⟶
x0
(
λ x8 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x9 :
ι →
ι →
ι → ι
.
λ x10 .
0
)
(
λ x8 :
(
ι → ι
)
→ ι
.
setsum
(
setsum
0
(
x5
(
λ x9 .
0
)
(
Inj0
0
)
0
)
)
(
x8
(
λ x9 .
x8
(
λ x10 .
0
)
)
)
)
⟶
x1
(
λ x8 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x9 .
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 .
x8
(
setsum
(
Inj1
(
setsum
0
0
)
)
0
)
(
λ x12 x13 .
setsum
(
Inj1
x12
)
(
setsum
0
(
Inj1
0
)
)
)
)
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 x10 x11 .
setsum
0
(
setsum
(
Inj1
(
setsum
0
0
)
)
(
setsum
(
setsum
0
0
)
x11
)
)
)
)
⟶
False
)
Known
536b2..
:
not
(
∀ x0 :
(
(
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→ ι
)
→
ι →
(
ι →
(
ι → ι
)
→ ι
)
→ ο
.
∀ x1 :
(
ι → ι
)
→
(
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
)
→
(
ι →
ι → ι
)
→
ι → ο
.
∀ x2 :
(
ι → ι
)
→
ι →
(
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ο
.
∀ x3 :
(
(
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
)
→
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→
ι →
ι → ο
.
(
∀ x4 x5 .
∀ x6 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
∀ x7 .
x2
(
λ x8 .
0
)
(
x6
(
λ x8 .
λ x9 :
ι → ι
.
Inj1
(
setsum
(
Inj1
0
)
(
setsum
0
0
)
)
)
)
(
λ x8 x9 :
ι → ι
.
λ x10 .
x7
)
(
λ x8 :
ι → ι
.
λ x9 .
Inj1
(
Inj0
(
setsum
(
setsum
0
0
)
0
)
)
)
⟶
x3
(
λ x8 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x10 .
setsum
x7
0
)
(
setsum
(
setsum
(
Inj0
(
setsum
0
0
)
)
x5
)
(
Inj0
0
)
)
(
setsum
0
x4
)
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
(
(
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→ ι
.
x3
(
λ x8 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x10 .
Inj1
(
x7
(
λ x11 :
ι → ι
.
setsum
(
setsum
0
0
)
(
x11
0
)
)
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
(
λ x11 .
x9
(
λ x12 x13 .
Inj0
0
)
(
λ x12 .
Inj1
0
)
0
)
)
)
(
setsum
0
(
Inj0
(
Inj0
(
setsum
0
0
)
)
)
)
(
Inj1
x6
)
⟶
In
(
setsum
(
Inj1
x6
)
x4
)
(
Inj1
x5
)
)
⟶
(
∀ x4 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x5 .
∀ x6 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
∀ x7 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→
ι →
ι → ι
.
In
(
Inj1
x5
)
(
setsum
0
(
Inj1
(
x7
(
λ x8 .
Inj1
0
)
(
λ x8 x9 .
setsum
0
0
)
0
0
)
)
)
⟶
x0
(
λ x8 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
0
)
(
Inj0
0
)
(
λ x8 .
λ x9 :
ι → ι
.
setsum
0
(
x7
(
λ x10 .
x10
)
(
λ x10 x11 .
x11
)
(
Inj0
(
x6
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
0
)
)
)
(
Inj0
0
)
)
)
⟶
x2
(
λ x8 .
x8
)
0
(
λ x8 x9 :
ι → ι
.
λ x10 .
0
)
(
λ x8 :
ι → ι
.
λ x9 .
x7
Inj1
(
λ x10 x11 .
x11
)
(
x8
(
setsum
(
x6
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
0
)
)
x9
)
)
0
)
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
(
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
In
(
Inj0
0
)
(
setsum
(
Inj1
0
)
(
Inj0
(
setsum
(
Inj1
0
)
x4
)
)
)
⟶
x2
(
λ x8 .
0
)
0
(
λ x8 x9 :
ι → ι
.
λ x10 .
Inj0
(
Inj0
(
Inj0
(
Inj1
0
)
)
)
)
(
λ x8 :
ι → ι
.
λ x9 .
setsum
x6
(
setsum
(
x7
(
λ x10 .
0
)
(
setsum
0
0
)
(
λ x10 .
setsum
0
0
)
(
Inj0
0
)
)
0
)
)
⟶
x3
(
λ x8 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x10 .
setsum
(
setsum
(
x9
(
λ x11 x12 .
0
)
(
λ x11 .
x8
(
λ x12 :
ι →
ι → ι
.
λ x13 :
ι → ι
.
0
)
)
(
Inj1
0
)
)
(
setsum
(
setsum
0
0
)
0
)
)
(
x9
(
λ x11 x12 .
x10
)
(
λ x11 .
Inj1
(
setsum
0
0
)
)
(
Inj1
(
Inj0
0
)
)
)
)
(
setsum
(
x7
(
λ x8 .
Inj1
(
x7
(
λ x9 .
0
)
0
(
λ x9 .
0
)
0
)
)
x5
(
λ x8 .
Inj1
0
)
(
Inj1
(
Inj1
0
)
)
)
x6
)
0
)
⟶
(
∀ x4 .
∀ x5 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x6 :
(
ι → ι
)
→ ι
.
∀ x7 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
In
(
Inj0
(
Inj1
(
setsum
0
(
Inj0
0
)
)
)
)
(
Inj1
(
setsum
(
setsum
(
setsum
0
0
)
0
)
(
x7
(
λ x8 .
x7
(
λ x9 .
0
)
(
λ x9 :
ι → ι
.
λ x10 .
0
)
)
(
λ x8 :
ι → ι
.
λ x9 .
Inj0
0
)
)
)
)
⟶
x3
(
λ x8 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x10 .
setsum
(
setsum
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
0
)
(
x7
(
λ x11 .
x10
)
(
λ x11 :
ι → ι
.
λ x12 .
x9
(
λ x13 x14 .
0
)
(
λ x13 .
setsum
0
0
)
(
setsum
0
0
)
)
)
)
(
Inj1
(
Inj1
(
setsum
(
Inj0
0
)
(
setsum
0
0
)
)
)
)
(
Inj0
x4
)
⟶
x1
(
λ x8 .
Inj1
(
x5
0
(
λ x9 :
ι → ι
.
λ x10 .
x10
)
)
)
(
λ x8 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
Inj0
(
Inj1
(
setsum
(
setsum
0
0
)
(
Inj1
0
)
)
)
)
(
λ x8 x9 .
Inj0
(
x7
(
λ x10 .
setsum
(
setsum
0
0
)
(
Inj0
0
)
)
(
λ x10 :
ι → ι
.
λ x11 .
Inj1
(
x10
0
)
)
)
)
(
x7
(
λ x8 .
0
)
(
λ x8 :
ι → ι
.
λ x9 .
setsum
(
x6
(
λ x10 .
0
)
)
0
)
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→ ι
.
∀ x5 x6 .
∀ x7 :
ι → ι
.
x1
(
λ x8 .
0
)
(
λ x8 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
(
λ x8 x9 .
Inj1
(
setsum
x6
x8
)
)
0
⟶
In
(
Inj1
(
setsum
0
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
)
(
Inj0
(
setsum
(
Inj1
x6
)
(
x4
(
λ x8 .
0
)
)
)
)
)
⟶
(
∀ x4 x5 x6 x7 .
In
x7
(
setsum
(
Inj0
(
setsum
0
(
setsum
0
0
)
)
)
x6
)
⟶
x2
(
λ x8 .
Inj0
(
setsum
(
Inj0
x8
)
(
setsum
(
setsum
0
0
)
0
)
)
)
(
Inj0
(
setsum
x5
0
)
)
(
λ x8 x9 :
ι → ι
.
λ x10 .
Inj0
(
Inj1
(
setsum
(
setsum
0
0
)
x7
)
)
)
(
λ x8 :
ι → ι
.
λ x9 .
Inj1
(
setsum
0
(
setsum
0
(
setsum
0
0
)
)
)
)
⟶
x0
(
λ x8 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
Inj0
x7
)
(
Inj1
x5
)
(
λ x8 .
λ x9 :
ι → ι
.
0
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
∀ x7 .
x0
(
λ x8 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
setsum
(
setsum
(
setsum
0
(
Inj0
0
)
)
0
)
(
Inj1
(
Inj1
(
setsum
0
0
)
)
)
)
(
setsum
(
Inj1
(
setsum
x5
0
)
)
x7
)
(
λ x8 .
λ x9 :
ι → ι
.
setsum
(
Inj1
(
setsum
(
x6
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
0
)
)
x8
)
)
x7
)
⟶
x1
(
setsum
(
Inj1
(
Inj1
x7
)
)
)
(
λ x8 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
(
λ x8 x9 .
setsum
x9
(
setsum
(
Inj1
(
setsum
0
0
)
)
x9
)
)
(
Inj0
(
x6
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
setsum
(
setsum
0
0
)
0
)
)
)
)
⟶
False
)
Known
57e52..
:
not
(
∀ x0 :
(
ι →
ι →
(
ι →
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
(
ι → ι
)
→
ι → ο
.
∀ x1 :
(
ι →
(
ι →
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ο
.
∀ x2 :
(
ι → ι
)
→
(
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι → ι
)
→ ο
.
∀ x3 :
(
ι → ι
)
→
ι → ο
.
(
∀ x4 :
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x5 x6 .
∀ x7 :
ι → ι
.
x0
(
λ x8 x9 .
λ x10 :
ι →
ι → ι
.
Inj1
0
)
(
λ x8 .
setsum
(
x7
(
setsum
0
x8
)
)
(
Inj0
0
)
)
(
λ x8 .
x8
)
(
x7
(
setsum
0
(
Inj0
0
)
)
)
⟶
x3
(
λ x8 .
setsum
x6
(
Inj1
0
)
)
(
Inj0
(
setsum
(
x7
0
)
(
setsum
(
Inj1
0
)
(
Inj1
0
)
)
)
)
)
⟶
(
∀ x4 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x5 x6 x7 .
In
(
x4
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
0
)
(
λ x8 :
ι → ι
.
λ x9 .
x8
0
)
(
λ x8 .
0
)
0
)
(
Inj1
(
Inj0
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
)
⟶
x3
(
λ x8 .
Inj1
0
)
0
⟶
x0
(
λ x8 x9 .
λ x10 :
ι →
ι → ι
.
Inj1
(
setsum
0
x9
)
)
(
λ x8 .
setsum
(
Inj1
(
Inj0
(
Inj1
0
)
)
)
(
Inj0
(
setsum
0
(
Inj1
0
)
)
)
)
(
λ x8 .
x8
)
(
Inj1
(
x4
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
Inj1
(
Inj1
0
)
)
(
λ x8 :
ι → ι
.
λ x9 .
Inj0
0
)
(
λ x8 .
0
)
x6
)
)
)
⟶
(
∀ x4 :
ι →
ι → ι
.
∀ x5 x6 x7 .
x3
(
λ x8 .
setsum
(
setsum
x6
x6
)
x7
)
(
Inj1
0
)
⟶
x2
(
λ x8 .
setsum
0
0
)
(
λ x8 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
0
)
(
λ x8 .
x6
)
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 .
∀ x7 :
ι → ι
.
x2
(
λ x8 .
setsum
x6
(
setsum
0
(
x5
0
)
)
)
(
λ x8 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
0
)
(
λ x8 .
setsum
0
(
x7
(
setsum
(
Inj1
0
)
(
Inj0
0
)
)
)
)
⟶
In
(
setsum
(
Inj0
(
x5
x4
)
)
0
)
(
Inj1
(
Inj1
(
setsum
0
0
)
)
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→ ι
.
∀ x5 :
(
ι →
ι → ι
)
→ ι
.
∀ x6 :
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
∀ x7 :
(
ι →
ι →
ι → ι
)
→
ι → ι
.
In
(
Inj0
(
Inj1
(
x5
(
λ x8 x9 .
0
)
)
)
)
(
x5
(
λ x8 x9 .
x6
(
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 :
ι → ι
.
setsum
(
x11
0
)
(
Inj0
0
)
)
)
)
⟶
x1
(
λ x8 .
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
λ x12 .
x10
)
(
λ x8 :
ι → ι
.
Inj0
(
x5
(
λ x9 x10 .
x9
)
)
)
⟶
x1
(
λ x8 .
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
λ x12 .
Inj0
x10
)
(
λ x8 :
ι → ι
.
Inj1
(
Inj0
(
x5
(
λ x9 x10 .
x8
0
)
)
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 :
ι →
ι → ι
.
∀ x6 .
∀ x7 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
In
(
x5
(
Inj1
(
setsum
(
setsum
0
0
)
(
x4
0
)
)
)
(
x7
(
λ x8 .
setsum
(
Inj0
0
)
(
x5
0
0
)
)
(
λ x8 x9 .
Inj1
(
setsum
0
0
)
)
)
)
x6
⟶
x1
(
λ x8 .
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
λ x12 .
setsum
(
Inj0
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
(
Inj1
(
x9
x10
(
λ x13 .
0
)
(
setsum
0
0
)
)
)
)
(
λ x8 :
ι → ι
.
Inj0
0
)
⟶
x0
(
λ x8 x9 .
λ x10 :
ι →
ι → ι
.
0
)
(
λ x8 .
x8
)
(
λ x8 .
x5
(
x7
(
λ x9 .
x9
)
(
λ x9 x10 .
x8
)
)
(
setsum
0
(
x7
(
λ x9 .
Inj0
0
)
(
λ x9 x10 .
setsum
0
0
)
)
)
)
0
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x5 :
ι →
ι →
(
ι → ι
)
→ ι
.
∀ x6 .
∀ x7 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
.
In
(
x7
(
λ x8 :
(
ι → ι
)
→ ι
.
0
)
)
(
Inj1
(
Inj1
(
x7
(
λ x8 :
(
ι → ι
)
→ ι
.
setsum
0
0
)
)
)
)
⟶
x1
(
λ x8 .
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
λ x12 .
Inj1
0
)
(
λ x8 :
ι → ι
.
x7
(
λ x9 :
(
ι → ι
)
→ ι
.
setsum
(
Inj1
0
)
0
)
)
⟶
x0
(
λ x8 x9 .
λ x10 :
ι →
ι → ι
.
0
)
(
λ x8 .
0
)
(
λ x8 .
Inj1
(
setsum
(
setsum
(
setsum
0
0
)
(
x5
0
0
(
λ x9 .
0
)
)
)
(
Inj1
(
x7
(
λ x9 :
(
ι → ι
)
→ ι
.
0
)
)
)
)
)
(
setsum
0
(
x7
(
λ x8 :
(
ι → ι
)
→ ι
.
Inj0
(
Inj0
0
)
)
)
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→ ι
.
∀ x5 :
(
(
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→
ι →
ι → ι
.
∀ x6 :
ι → ι
.
∀ x7 .
x0
(
λ x8 x9 .
λ x10 :
ι →
ι → ι
.
setsum
x9
(
Inj0
(
x10
(
setsum
0
0
)
0
)
)
)
(
λ x8 .
x5
(
λ x9 :
ι → ι
.
setsum
(
Inj1
0
)
(
setsum
(
setsum
0
0
)
0
)
)
(
λ x9 x10 .
0
)
(
Inj1
(
setsum
(
setsum
0
0
)
(
x6
0
)
)
)
0
)
(
λ x8 .
0
)
(
Inj0
(
x5
(
λ x8 :
ι → ι
.
0
)
(
λ x8 x9 .
Inj0
0
)
(
setsum
0
(
x4
(
λ x8 .
0
)
)
)
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
)
⟶
x1
(
λ x8 .
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
λ x12 .
setsum
x12
(
Inj1
x12
)
)
(
λ x8 :
ι → ι
.
Inj0
(
setsum
(
Inj0
0
)
0
)
)
)
⟶
False
)
Known
ead0e..
:
not
(
∀ x0 :
(
ι →
ι → ι
)
→
(
(
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ο
.
∀ x1 :
(
(
ι → ι
)
→
ι →
ι → ι
)
→
ι → ο
.
∀ x2 :
(
ι →
(
ι →
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
)
→
ι →
(
(
ι → ι
)
→
ι → ι
)
→
ι → ο
.
∀ x3 :
(
(
(
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
ι → ο
.
(
∀ x4 x5 .
∀ x6 :
(
ι → ι
)
→ ι
.
∀ x7 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
x1
(
λ x8 :
ι → ι
.
λ x9 x10 .
Inj1
(
Inj1
(
Inj1
(
Inj0
0
)
)
)
)
0
⟶
x3
(
λ x8 :
(
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x9 .
Inj0
(
x6
(
λ x10 .
setsum
(
setsum
0
0
)
0
)
)
)
(
Inj0
0
)
)
⟶
(
∀ x4 :
(
ι →
(
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x5 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
∀ x6 x7 .
x3
(
λ x8 :
(
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x9 .
x9
)
(
setsum
0
(
setsum
(
setsum
(
Inj0
0
)
0
)
(
x5
(
λ x8 .
x5
(
λ x9 .
0
)
(
λ x9 x10 .
0
)
)
(
λ x8 x9 .
0
)
)
)
)
⟶
x3
(
λ x8 :
(
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x9 .
x9
)
(
Inj1
0
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
ι → ι
.
∀ x6 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x7 :
ι → ι
.
x2
(
λ x8 .
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x10 x11 .
x8
)
(
setsum
(
Inj1
0
)
(
setsum
(
setsum
(
setsum
0
0
)
0
)
(
Inj1
(
setsum
0
0
)
)
)
)
(
λ x8 :
ι → ι
.
λ x9 .
setsum
(
x8
(
Inj0
(
Inj0
0
)
)
)
(
Inj1
(
Inj1
(
setsum
0
0
)
)
)
)
(
Inj0
(
Inj1
(
setsum
(
setsum
0
0
)
x4
)
)
)
⟶
x2
(
λ x8 .
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x10 x11 .
0
)
(
setsum
(
x7
(
setsum
x4
(
Inj1
0
)
)
)
x4
)
(
λ x8 :
ι → ι
.
λ x9 .
x9
)
(
Inj1
(
setsum
0
(
Inj0
(
x7
0
)
)
)
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x5 :
(
ι → ι
)
→ ι
.
∀ x6 .
∀ x7 :
ι → ι
.
x2
(
λ x8 .
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x10 x11 .
setsum
(
setsum
x8
(
x9
(
Inj1
0
)
(
λ x12 .
x11
)
0
)
)
0
)
(
Inj1
(
setsum
(
x4
(
λ x8 .
0
)
(
λ x8 .
x8
)
)
0
)
)
(
λ x8 :
ι → ι
.
λ x9 .
setsum
(
setsum
(
x7
(
Inj1
0
)
)
(
x7
(
Inj0
0
)
)
)
(
Inj1
(
x8
0
)
)
)
(
x5
(
λ x8 .
Inj1
0
)
)
⟶
x1
(
λ x8 :
ι → ι
.
λ x9 x10 .
0
)
(
Inj0
(
Inj1
(
setsum
0
(
Inj0
0
)
)
)
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
∀ x5 :
(
ι → ι
)
→
ι → ι
.
∀ x6 .
∀ x7 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
x2
(
λ x8 .
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x10 x11 .
0
)
0
(
λ x8 :
ι → ι
.
λ x9 .
0
)
(
setsum
0
0
)
⟶
x1
(
λ x8 :
ι → ι
.
λ x9 x10 .
Inj1
0
)
(
x7
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
λ x9 :
ι → ι
.
λ x10 .
setsum
(
Inj0
0
)
0
)
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
(
ι → ι
)
→
ι →
ι → ι
.
∀ x7 .
In
(
Inj0
x4
)
(
setsum
0
(
x6
(
λ x8 .
setsum
(
Inj0
0
)
(
setsum
0
0
)
)
(
setsum
x4
(
Inj1
0
)
)
0
)
)
⟶
x1
(
λ x8 :
ι → ι
.
λ x9 x10 .
x10
)
0
⟶
x2
(
λ x8 .
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x10 x11 .
setsum
0
x8
)
(
x6
(
λ x8 .
setsum
(
setsum
x8
x8
)
0
)
0
(
setsum
x4
(
Inj0
x5
)
)
)
(
λ x8 :
ι → ι
.
λ x9 .
Inj1
0
)
(
setsum
0
(
Inj1
x7
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 .
∀ x6 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x7 .
In
(
x6
0
(
λ x8 :
ι → ι
.
Inj0
0
)
)
x7
⟶
x0
(
λ x8 x9 .
setsum
x9
x9
)
(
λ x8 :
ι → ι
.
λ x9 :
(
ι → ι
)
→ ι
.
x9
(
λ x10 .
setsum
(
Inj1
(
Inj1
0
)
)
0
)
)
⟶
x0
(
λ x8 x9 .
setsum
x9
(
setsum
(
Inj0
(
setsum
0
0
)
)
(
Inj1
(
x6
0
(
λ x10 :
ι → ι
.
0
)
)
)
)
)
(
λ x8 :
ι → ι
.
λ x9 :
(
ι → ι
)
→ ι
.
0
)
)
⟶
(
∀ x4 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
∀ x5 :
ι → ι
.
∀ x6 x7 .
x0
(
λ x8 x9 .
Inj0
0
)
(
λ x8 :
ι → ι
.
λ x9 :
(
ι → ι
)
→ ι
.
Inj0
0
)
⟶
In
(
Inj1
(
setsum
0
(
x4
(
λ x8 :
ι → ι
.
x6
)
(
λ x8 .
x5
0
)
)
)
)
x7
)
⟶
False
)
Known
bc887..
:
not
(
∀ x0 :
(
ι →
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι →
ι → ο
.
∀ x1 :
(
ι →
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι → ο
.
∀ x2 :
(
ι → ι
)
→
(
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→
ι → ο
.
∀ x3 :
(
ι →
(
ι →
ι → ι
)
→ ι
)
→
ι →
ι → ο
.
(
∀ x4 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x5 x6 x7 .
In
(
Inj0
x6
)
(
setsum
(
setsum
0
0
)
(
setsum
x6
(
Inj0
(
setsum
0
0
)
)
)
)
⟶
x2
(
λ x8 .
Inj0
(
Inj0
0
)
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
ι →
ι → ι
.
λ x10 x11 .
x10
)
(
setsum
(
x4
(
λ x8 :
ι →
ι → ι
.
λ x9 :
ι → ι
.
λ x10 .
Inj0
(
setsum
0
0
)
)
)
0
)
⟶
x3
(
λ x8 .
λ x9 :
ι →
ι → ι
.
Inj0
x8
)
x5
(
setsum
(
setsum
(
setsum
0
(
setsum
0
0
)
)
(
Inj0
0
)
)
0
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
∀ x5 :
ι → ι
.
∀ x6 x7 .
x3
(
λ x8 .
λ x9 :
ι →
ι → ι
.
0
)
x7
(
setsum
(
setsum
(
setsum
(
setsum
0
0
)
0
)
(
setsum
(
setsum
0
0
)
(
Inj0
0
)
)
)
(
setsum
0
(
Inj1
(
setsum
0
0
)
)
)
)
⟶
x3
(
λ x8 .
λ x9 :
ι →
ι → ι
.
x7
)
(
setsum
(
x4
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
x7
)
)
x6
)
(
Inj0
(
Inj1
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x6 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
∀ x7 .
In
(
Inj0
0
)
(
setsum
0
(
x5
(
Inj0
(
setsum
0
0
)
)
(
λ x8 :
ι → ι
.
λ x9 .
Inj0
0
)
)
)
⟶
x0
(
λ x8 x9 .
λ x10 :
(
ι → ι
)
→
ι → ι
.
x8
)
x7
(
x6
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
λ x9 :
ι → ι
.
λ x10 .
Inj1
0
)
(
λ x8 x9 .
0
)
)
⟶
x2
(
λ x8 .
x8
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
ι →
ι → ι
.
λ x10 x11 .
x10
)
(
setsum
(
Inj0
0
)
(
x6
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
λ x9 :
ι → ι
.
λ x10 .
Inj0
0
)
(
λ x8 x9 .
x9
)
)
)
)
⟶
(
∀ x4 :
ι →
ι → ι
.
∀ x5 :
ι → ι
.
∀ x6 .
∀ x7 :
ι → ι
.
In
(
Inj0
(
Inj1
0
)
)
(
setsum
(
setsum
(
Inj0
0
)
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
(
setsum
0
(
setsum
(
Inj0
0
)
(
x4
0
0
)
)
)
)
⟶
x2
(
λ x8 .
0
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
ι →
ι → ι
.
λ x10 x11 .
0
)
(
setsum
(
setsum
0
(
setsum
(
setsum
0
0
)
(
Inj0
0
)
)
)
(
Inj1
x6
)
)
⟶
x1
(
λ x8 .
λ x9 :
(
ι → ι
)
→ ι
.
Inj0
0
)
(
x4
0
(
x5
(
setsum
(
Inj1
0
)
0
)
)
)
)
⟶
(
∀ x4 .
∀ x5 x6 :
ι → ι
.
∀ x7 .
x3
(
λ x8 .
λ x9 :
ι →
ι → ι
.
0
)
0
0
⟶
x1
(
λ x8 .
λ x9 :
(
ι → ι
)
→ ι
.
x9
(
λ x10 .
setsum
(
Inj1
(
Inj0
0
)
)
(
setsum
0
0
)
)
)
0
)
⟶
(
∀ x4 x5 x6 x7 .
In
(
Inj0
x6
)
(
setsum
(
setsum
x4
(
setsum
x5
(
setsum
0
0
)
)
)
(
Inj1
(
setsum
x5
0
)
)
)
⟶
x1
(
λ x8 .
λ x9 :
(
ι → ι
)
→ ι
.
x7
)
0
⟶
x2
(
λ x8 .
0
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
ι →
ι → ι
.
λ x10 x11 .
setsum
0
0
)
x5
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
∀ x5 x6 x7 .
In
(
Inj1
0
)
x5
⟶
x1
(
λ x8 .
λ x9 :
(
ι → ι
)
→ ι
.
0
)
0
⟶
x0
(
λ x8 x9 .
λ x10 :
(
ι → ι
)
→
ι → ι
.
Inj1
0
)
(
Inj1
(
Inj1
(
x4
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
0
)
)
)
)
(
Inj1
(
setsum
(
setsum
(
Inj0
0
)
0
)
(
Inj1
(
Inj0
0
)
)
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 .
∀ x6 :
ι → ι
.
∀ x7 .
x0
(
λ x8 x9 .
λ x10 :
(
ι → ι
)
→
ι → ι
.
0
)
(
x4
0
)
x7
⟶
False
)
⟶
False
)
Known
1cb9d..
:
not
(
∀ x0 :
(
(
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι → ο
.
∀ x1 :
(
(
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι →
ι →
ι →
ι → ι
)
→
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ο
.
∀ x2 :
(
ι → ι
)
→
(
ι → ι
)
→
(
ι →
(
ι → ι
)
→ ι
)
→ ο
.
∀ x3 :
(
ι →
(
ι →
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→
ι →
ι →
ι →
(
ι → ι
)
→
ι → ο
.
(
∀ x4 x5 x6 x7 .
x2
(
λ x8 .
setsum
x5
0
)
(
λ x8 .
0
)
(
λ x8 .
λ x9 :
ι → ι
.
setsum
0
x8
)
⟶
x3
(
λ x8 .
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x10 .
x7
)
x5
(
Inj0
0
)
(
Inj1
(
Inj0
(
setsum
(
Inj1
0
)
(
setsum
0
0
)
)
)
)
(
λ x8 .
0
)
x7
)
⟶
(
∀ x4 .
∀ x5 :
(
ι →
ι →
ι → ι
)
→
ι →
ι → ι
.
∀ x6 :
(
ι → ι
)
→ ι
.
∀ x7 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
x3
(
λ x8 .
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x10 .
setsum
x8
(
Inj0
0
)
)
0
(
setsum
0
0
)
0
(
λ x8 .
Inj1
(
Inj0
(
Inj0
(
setsum
0
0
)
)
)
)
(
setsum
(
setsum
(
x5
(
λ x8 x9 x10 .
x10
)
(
setsum
0
0
)
0
)
0
)
(
setsum
(
x5
(
λ x8 x9 x10 .
Inj0
0
)
0
0
)
0
)
)
⟶
In
(
x5
(
λ x8 x9 x10 .
Inj1
(
Inj0
(
setsum
0
0
)
)
)
(
Inj1
(
x7
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
x6
(
λ x9 .
0
)
)
(
setsum
0
0
)
(
x7
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
0
)
0
0
)
)
)
(
x7
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
0
)
(
x5
(
λ x8 x9 x10 .
0
)
0
(
Inj0
0
)
)
(
Inj1
x4
)
)
)
(
Inj1
(
Inj0
(
Inj0
x4
)
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 x6 .
∀ x7 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
x0
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
0
)
(
setsum
(
x7
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
Inj1
0
)
(
λ x8 :
ι → ι
.
setsum
(
x8
0
)
0
)
(
setsum
(
setsum
0
0
)
)
(
setsum
(
x4
0
)
(
Inj1
0
)
)
)
(
Inj1
(
setsum
(
setsum
0
0
)
x5
)
)
)
⟶
x2
(
λ x8 .
Inj1
0
)
(
λ x8 .
0
)
(
λ x8 .
λ x9 :
ι → ι
.
0
)
)
⟶
(
∀ x4 x5 .
∀ x6 x7 :
ι → ι
.
x2
(
λ x8 .
0
)
(
λ x8 .
0
)
(
λ x8 .
λ x9 :
ι → ι
.
x8
)
⟶
x2
(
λ x8 .
Inj0
(
Inj0
(
x6
(
setsum
0
0
)
)
)
)
(
λ x8 .
0
)
(
λ x8 .
λ x9 :
ι → ι
.
0
)
)
⟶
(
∀ x4 :
ι →
(
ι →
ι → ι
)
→
ι →
ι → ι
.
∀ x5 .
∀ x6 x7 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
In
(
Inj0
(
x4
(
Inj1
(
Inj1
0
)
)
(
λ x8 x9 .
x6
0
(
λ x10 :
ι → ι
.
λ x11 .
Inj1
0
)
)
(
setsum
0
(
Inj1
0
)
)
0
)
)
(
x7
(
setsum
(
x7
(
setsum
0
0
)
(
λ x8 :
ι → ι
.
λ x9 .
setsum
0
0
)
)
(
setsum
(
x4
0
(
λ x8 x9 .
0
)
0
0
)
(
Inj0
0
)
)
)
(
λ x8 :
ι → ι
.
λ x9 .
setsum
(
Inj0
(
Inj1
0
)
)
0
)
)
⟶
x0
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
x7
0
(
λ x9 :
ι → ι
.
λ x10 .
Inj0
(
Inj1
0
)
)
)
(
setsum
(
x7
(
setsum
(
setsum
0
0
)
(
x4
0
(
λ x8 x9 .
0
)
0
0
)
)
(
λ x8 :
ι → ι
.
λ x9 .
x6
0
(
λ x10 :
ι → ι
.
λ x11 .
setsum
0
0
)
)
)
x5
)
⟶
x1
(
λ x8 :
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
setsum
(
Inj1
(
Inj1
0
)
)
(
Inj1
(
Inj1
0
)
)
)
(
λ x8 x9 x10 x11 .
0
)
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
setsum
(
setsum
(
Inj0
0
)
0
)
(
Inj1
(
Inj1
x10
)
)
)
)
⟶
(
∀ x4 :
(
ι →
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x5 x6 :
ι →
ι → ι
.
∀ x7 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
x1
(
λ x8 :
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
x6
(
Inj1
(
setsum
(
Inj0
0
)
(
x7
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 .
0
)
(
λ x9 :
ι → ι
.
λ x10 .
0
)
0
0
)
)
)
(
setsum
(
Inj0
(
setsum
0
0
)
)
(
setsum
(
Inj0
0
)
0
)
)
)
(
λ x8 x9 x10 x11 .
x8
)
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
0
)
⟶
x3
(
λ x8 .
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
Inj0
)
(
Inj0
(
x7
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
setsum
(
Inj0
0
)
(
Inj1
0
)
)
(
λ x8 :
ι → ι
.
λ x9 .
Inj1
0
)
0
(
Inj0
0
)
)
)
(
setsum
(
setsum
(
x6
(
Inj0
0
)
(
x4
(
λ x8 x9 .
0
)
(
λ x8 :
ι → ι
.
λ x9 .
0
)
)
)
0
)
(
x6
0
(
Inj1
(
Inj1
0
)
)
)
)
(
Inj0
(
Inj1
(
setsum
(
x6
0
0
)
(
Inj0
0
)
)
)
)
(
λ x8 .
x8
)
(
setsum
(
setsum
0
(
Inj0
(
setsum
0
0
)
)
)
(
x7
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
setsum
0
0
)
(
λ x8 :
ι → ι
.
λ x9 .
Inj0
(
Inj0
0
)
)
(
Inj1
(
x4
(
λ x8 x9 .
0
)
(
λ x8 :
ι → ι
.
λ x9 .
0
)
)
)
(
setsum
(
setsum
0
0
)
(
x4
(
λ x8 x9 .
0
)
(
λ x8 :
ι → ι
.
λ x9 .
0
)
)
)
)
)
)
⟶
(
∀ x4 :
(
(
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
∀ x5 .
∀ x6 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x7 .
In
(
setsum
(
setsum
0
(
Inj0
(
Inj0
0
)
)
)
(
x4
(
λ x8 :
ι → ι
.
λ x9 x10 .
Inj0
(
Inj0
0
)
)
)
)
(
x4
(
λ x8 :
ι → ι
.
λ x9 x10 .
0
)
)
⟶
x3
(
λ x8 .
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x10 .
Inj0
(
setsum
x8
x7
)
)
(
Inj0
x7
)
(
Inj0
(
setsum
x7
0
)
)
(
Inj0
(
setsum
(
Inj1
0
)
(
setsum
x5
x7
)
)
)
(
λ x8 .
x8
)
0
⟶
x0
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
x5
)
(
setsum
(
Inj0
0
)
(
Inj0
0
)
)
)
⟶
(
∀ x4 :
ι →
ι → ι
.
∀ x5 :
(
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
∀ x6 x7 .
In
(
Inj0
(
Inj1
(
x5
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
λ x9 x10 .
Inj1
0
)
)
)
)
(
Inj1
(
x4
(
Inj1
0
)
(
setsum
(
setsum
0
0
)
0
)
)
)
⟶
x0
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
0
)
(
Inj1
x7
)
⟶
x1
(
λ x8 :
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
setsum
x7
0
)
(
λ x8 x9 x10 x11 .
setsum
(
Inj0
x9
)
x9
)
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
Inj0
(
setsum
(
x9
0
)
0
)
)
)
⟶
False
)
Known
44176..
:
not
(
∀ x0 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι →
ι → ι
)
→
ι → ο
.
∀ x1 :
(
ι →
(
(
ι →
ι → ι
)
→ ι
)
→ ι
)
→
(
ι →
ι →
ι → ι
)
→ ο
.
∀ x2 :
(
ι →
ι → ι
)
→
ι → ο
.
∀ x3 :
(
(
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
)
→
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
)
→
ι →
ι → ο
.
(
∀ x4 .
∀ x5 :
ι →
(
ι → ι
)
→ ι
.
∀ x6 x7 .
In
x6
(
setsum
x6
(
Inj1
(
Inj1
(
Inj1
0
)
)
)
)
⟶
x3
(
λ x8 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
λ x9 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
setsum
(
Inj0
0
)
0
)
x4
(
Inj0
0
)
)
⟶
(
∀ x4 :
(
ι →
ι → ι
)
→
ι → ι
.
∀ x5 .
∀ x6 :
ι → ι
.
∀ x7 .
In
(
Inj1
(
setsum
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
x7
)
)
(
Inj0
(
setsum
(
x6
x7
)
x7
)
)
⟶
x3
(
λ x8 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
λ x9 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
Inj1
(
setsum
0
0
)
)
0
(
Inj0
(
Inj0
(
setsum
(
setsum
0
0
)
(
Inj0
0
)
)
)
)
⟶
x2
(
λ x8 x9 .
0
)
(
setsum
(
Inj0
0
)
(
setsum
(
x6
0
)
(
x6
(
x4
(
λ x8 x9 .
0
)
0
)
)
)
)
)
⟶
(
∀ x4 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι →
ι → ι
.
∀ x5 :
ι →
(
ι → ι
)
→ ι
.
∀ x6 :
(
ι →
(
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
∀ x7 :
(
ι →
(
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
In
(
x5
0
Inj1
)
(
Inj1
(
x4
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
Inj0
(
Inj1
0
)
)
(
λ x8 .
0
)
(
setsum
0
0
)
0
)
)
⟶
x2
(
λ x8 x9 .
Inj1
(
setsum
(
x6
(
λ x10 .
λ x11 :
ι → ι
.
Inj1
0
)
(
λ x10 x11 .
0
)
)
(
x6
(
λ x10 .
λ x11 :
ι → ι
.
0
)
(
λ x10 x11 .
x9
)
)
)
)
(
setsum
(
setsum
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
(
setsum
(
Inj1
0
)
(
Inj1
0
)
)
)
0
)
)
⟶
(
∀ x4 :
ι →
(
ι → ι
)
→ ι
.
∀ x5 .
∀ x6 :
(
(
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
∀ x7 .
x2
(
λ x8 x9 .
setsum
x9
(
Inj1
(
setsum
(
setsum
0
0
)
0
)
)
)
(
setsum
(
x4
(
setsum
(
Inj1
0
)
(
setsum
0
0
)
)
(
λ x8 .
Inj0
x5
)
)
(
setsum
(
x4
(
Inj1
0
)
(
λ x8 .
Inj0
0
)
)
(
Inj1
0
)
)
)
⟶
x3
(
λ x8 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
λ x9 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
Inj0
(
x8
(
λ x10 .
0
)
(
λ x10 :
ι → ι
.
λ x11 .
0
)
0
(
Inj1
(
Inj1
0
)
)
)
)
(
setsum
(
setsum
(
Inj0
(
setsum
0
0
)
)
x7
)
x5
)
0
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 .
∀ x7 :
(
ι → ι
)
→
ι → ι
.
In
(
Inj0
(
x7
(
λ x8 .
0
)
0
)
)
(
Inj1
(
Inj0
x4
)
)
⟶
x1
(
λ x8 .
λ x9 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x8 x9 x10 .
0
)
)
⟶
(
∀ x4 x5 .
∀ x6 x7 :
ι → ι
.
In
(
setsum
0
(
setsum
(
x7
0
)
x5
)
)
(
Inj1
0
)
⟶
x1
(
λ x8 .
λ x9 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x8 x9 x10 .
Inj1
0
)
⟶
x1
(
λ x8 .
λ x9 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x8 x9 x10 .
Inj1
x8
)
)
⟶
(
∀ x4 :
ι →
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
∀ x5 x6 .
∀ x7 :
(
ι → ι
)
→ ι
.
In
(
x4
(
Inj0
(
Inj1
x5
)
)
(
λ x8 :
ι → ι
.
setsum
(
x7
(
λ x9 .
x8
0
)
)
(
x8
(
setsum
0
0
)
)
)
(
λ x8 .
0
)
)
(
setsum
(
Inj1
x6
)
x6
)
⟶
x2
(
λ x8 .
Inj1
)
(
x7
(
λ x8 .
x7
(
λ x9 .
0
)
)
)
⟶
x0
(
λ x8 .
0
)
(
λ x8 :
ι → ι
.
λ x9 x10 .
setsum
(
setsum
(
Inj0
x9
)
(
Inj1
(
Inj1
0
)
)
)
(
Inj0
(
setsum
(
Inj0
0
)
(
x8
0
)
)
)
)
(
setsum
x5
(
setsum
(
setsum
0
(
Inj1
0
)
)
(
x4
0
(
λ x8 :
ι → ι
.
Inj0
0
)
(
λ x8 .
x6
)
)
)
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
∀ x5 :
(
(
ι →
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x6 x7 .
x0
(
λ x8 .
0
)
(
λ x8 :
ι → ι
.
λ x9 .
setsum
0
)
x6
⟶
x0
(
λ x8 .
x7
)
(
λ x8 :
ι → ι
.
λ x9 x10 .
x7
)
(
setsum
(
Inj0
(
Inj1
(
x4
(
λ x8 :
(
ι → ι
)
→ ι
.
0
)
(
λ x8 .
0
)
)
)
)
(
x4
(
λ x8 :
(
ι → ι
)
→ ι
.
0
)
Inj1
)
)
)
⟶
False
)
Known
c6930..
:
not
(
∀ x0 :
(
ι →
ι → ι
)
→
(
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι → ο
.
∀ x1 :
(
ι → ι
)
→
(
(
ι →
ι →
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ο
.
∀ x2 :
(
ι → ι
)
→
(
ι →
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι →
ι →
ι → ο
.
∀ x3 :
(
(
ι → ι
)
→
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
(
(
ι →
ι → ι
)
→ ι
)
→ ι
)
→
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ο
.
(
∀ x4 :
(
(
ι →
ι → ι
)
→ ι
)
→ ι
.
∀ x5 x6 x7 .
In
(
setsum
x5
(
Inj0
x6
)
)
(
setsum
0
(
x4
(
λ x8 :
ι →
ι → ι
.
Inj0
(
Inj0
0
)
)
)
)
⟶
x0
(
λ x8 x9 .
0
)
(
λ x8 :
ι →
(
ι → ι
)
→
ι → ι
.
0
)
(
setsum
0
(
Inj0
(
setsum
x6
(
Inj0
0
)
)
)
)
⟶
x3
(
λ x8 :
ι → ι
.
λ x9 .
λ x10 :
(
ι → ι
)
→
ι → ι
.
x7
)
(
λ x8 :
(
ι →
ι → ι
)
→ ι
.
x6
)
(
λ x8 :
(
ι → ι
)
→ ι
.
Inj1
0
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 x6 .
∀ x7 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
x3
(
λ x8 :
ι → ι
.
λ x9 .
λ x10 :
(
ι → ι
)
→
ι → ι
.
x9
)
(
λ x8 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x8 :
(
ι → ι
)
→ ι
.
Inj1
x6
)
⟶
In
(
Inj0
0
)
(
setsum
(
setsum
x6
(
setsum
x5
0
)
)
(
Inj0
(
setsum
x6
(
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 :
(
(
ι →
ι → ι
)
→ ι
)
→ ι
.
∀ x5 .
∀ x6 :
(
(
ι →
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→
ι → ι
.
∀ x7 :
(
ι →
ι →
ι → ι
)
→
ι → ι
.
In
(
x4
(
λ x8 :
ι →
ι → ι
.
x7
(
λ x9 x10 x11 .
x10
)
0
)
)
(
Inj1
(
x7
(
λ x8 x9 x10 .
0
)
(
setsum
0
(
Inj0
0
)
)
)
)
⟶
x1
(
λ x8 .
Inj1
(
Inj1
0
)
)
(
λ x8 :
ι →
ι →
ι → ι
.
setsum
0
(
Inj1
(
setsum
(
setsum
0
0
)
(
x8
0
0
0
)
)
)
)
(
λ x8 .
setsum
(
x7
(
λ x9 x10 x11 .
0
)
(
Inj1
x8
)
)
(
Inj1
x8
)
)
(
λ x8 :
ι → ι
.
0
)
(
λ x8 .
x5
)
⟶
x2
(
λ x8 .
setsum
(
setsum
0
(
Inj0
x5
)
)
(
Inj1
0
)
)
(
λ x8 .
λ x9 :
(
ι → ι
)
→ ι
.
Inj1
(
x9
(
λ x10 .
0
)
)
)
(
Inj0
(
x4
(
λ x8 :
ι →
ι → ι
.
0
)
)
)
(
setsum
0
0
)
(
setsum
(
x7
(
λ x8 x9 x10 .
setsum
(
Inj0
0
)
(
setsum
0
0
)
)
(
x6
(
λ x8 :
ι →
ι → ι
.
setsum
0
0
)
(
λ x8 x9 .
x7
(
λ x10 x11 x12 .
0
)
0
)
(
setsum
0
0
)
)
)
(
x4
(
λ x8 :
ι →
ι → ι
.
x7
(
λ x9 x10 x11 .
setsum
0
0
)
(
x6
(
λ x9 :
ι →
ι → ι
.
0
)
(
λ x9 x10 .
0
)
0
)
)
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 .
∀ x6 :
ι → ι
.
∀ x7 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
ι →
ι →
ι → ι
.
In
(
Inj0
(
Inj1
(
setsum
(
x4
0
)
(
setsum
0
0
)
)
)
)
(
Inj0
0
)
⟶
x2
(
λ x8 .
Inj0
(
x7
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 .
setsum
(
Inj1
0
)
0
)
0
(
x6
(
Inj1
0
)
)
0
)
)
(
λ x8 .
λ x9 :
(
ι → ι
)
→ ι
.
0
)
(
Inj1
(
x4
(
Inj0
0
)
)
)
(
x6
(
setsum
(
x7
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
setsum
0
0
)
(
Inj1
0
)
(
x7
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
0
)
0
0
0
)
0
)
(
x7
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
setsum
0
0
)
(
setsum
0
0
)
(
x6
0
)
0
)
)
)
(
setsum
(
x7
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
Inj0
0
)
(
x4
(
x6
0
)
)
(
setsum
(
Inj1
0
)
(
Inj1
0
)
)
0
)
(
Inj0
(
x4
0
)
)
)
⟶
x2
(
λ x8 .
setsum
0
(
Inj0
(
x6
(
setsum
0
0
)
)
)
)
(
λ x8 .
λ x9 :
(
ι → ι
)
→ ι
.
x8
)
(
Inj0
(
x6
(
setsum
0
(
setsum
0
0
)
)
)
)
(
Inj0
x5
)
(
Inj0
(
setsum
x5
(
x4
(
x4
0
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
(
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
)
→
ι →
ι →
ι → ι
.
∀ x6 :
ι →
ι →
ι → ι
.
∀ x7 .
x1
(
λ x8 .
Inj0
(
setsum
(
Inj1
(
Inj1
0
)
)
x8
)
)
(
λ x8 :
ι →
ι →
ι → ι
.
Inj1
(
x5
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 x11 .
0
)
0
0
0
)
)
(
λ x8 .
setsum
0
(
Inj1
(
Inj1
x7
)
)
)
(
λ x8 :
ι → ι
.
0
)
(
λ x8 .
0
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
(
ι → ι
)
→ ι
.
∀ x6 :
ι →
ι → ι
.
∀ x7 :
ι → ι
.
x1
(
λ x8 .
x5
(
Inj1
(
setsum
0
(
Inj1
0
)
)
)
(
λ x9 .
setsum
(
setsum
(
Inj1
0
)
x9
)
x8
)
)
(
λ x8 :
ι →
ι →
ι → ι
.
Inj0
(
Inj0
(
Inj0
(
x7
0
)
)
)
)
(
λ x8 .
Inj1
(
Inj0
(
setsum
(
Inj0
0
)
(
x6
0
0
)
)
)
)
(
λ x8 :
ι → ι
.
x6
(
setsum
(
x6
0
(
setsum
0
0
)
)
(
x6
(
Inj0
0
)
(
x8
0
)
)
)
(
Inj0
(
setsum
(
setsum
0
0
)
(
Inj0
0
)
)
)
)
(
λ x8 .
0
)
⟶
x1
(
λ x8 .
x6
(
Inj1
(
x5
0
(
λ x9 .
x8
)
)
)
0
)
(
λ x8 :
ι →
ι →
ι → ι
.
setsum
(
Inj0
(
Inj0
(
Inj1
0
)
)
)
0
)
(
λ x8 .
Inj0
(
setsum
(
setsum
(
Inj0
0
)
(
x7
0
)
)
0
)
)
(
λ x8 :
ι → ι
.
0
)
(
λ x8 .
0
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x6 x7 .
In
x7
x4
⟶
x0
(
λ x8 .
Inj0
)
(
λ x8 :
ι →
(
ι → ι
)
→
ι → ι
.
Inj0
(
setsum
x7
0
)
)
(
Inj0
(
x5
(
Inj0
x7
)
(
λ x8 x9 .
0
)
(
λ x8 .
0
)
)
)
⟶
x0
(
λ x8 x9 .
Inj0
x8
)
(
λ x8 :
ι →
(
ι → ι
)
→
ι → ι
.
Inj1
x6
)
(
setsum
(
setsum
0
(
Inj1
x6
)
)
(
setsum
(
Inj1
0
)
(
setsum
0
(
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
∀ x6 x7 .
x0
(
λ x8 x9 .
setsum
x7
x6
)
(
λ x8 :
ι →
(
ι → ι
)
→
ι → ι
.
Inj1
(
x8
x7
(
λ x9 .
setsum
x6
(
x8
0
(
λ x10 .
0
)
0
)
)
0
)
)
(
Inj0
(
x4
(
x4
(
Inj1
0
)
)
)
)
⟶
In
(
Inj1
(
setsum
(
x4
(
setsum
0
0
)
)
(
x4
(
setsum
0
0
)
)
)
)
(
Inj1
(
Inj0
0
)
)
)
⟶
False
)
Known
002b6..
:
not
(
∀ x0 :
(
(
ι → ι
)
→
ι →
(
ι →
ι → ι
)
→ ι
)
→
ι → ο
.
∀ x1 :
(
ι →
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ο
.
∀ x2 :
(
(
(
ι →
(
ι → ι
)
→ ι
)
→ ι
)
→
(
(
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
ι → ο
.
∀ x3 :
(
(
(
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→ ι
)
→ ι
)
→
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ο
.
(
∀ x4 .
∀ x5 :
ι →
ι → ι
.
∀ x6 .
∀ x7 :
ι → ι
.
x2
(
λ x8 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x10 .
Inj1
0
)
(
Inj1
(
setsum
(
Inj0
0
)
(
x5
0
(
Inj0
0
)
)
)
)
⟶
x3
(
λ x8 :
(
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
x6
)
(
λ x8 :
(
ι → ι
)
→ ι
.
0
)
)
⟶
(
∀ x4 .
∀ x5 x6 :
ι → ι
.
∀ x7 .
x3
(
λ x8 :
(
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
setsum
x7
(
setsum
(
x6
(
setsum
0
0
)
)
0
)
)
(
λ x8 :
(
ι → ι
)
→ ι
.
setsum
(
x8
(
λ x9 .
0
)
)
(
Inj1
(
Inj0
(
Inj0
0
)
)
)
)
⟶
x0
(
λ x8 :
ι → ι
.
λ x9 .
λ x10 :
ι →
ι → ι
.
setsum
0
x7
)
(
setsum
(
Inj1
0
)
(
setsum
(
Inj0
0
)
(
Inj1
(
Inj1
0
)
)
)
)
)
⟶
(
∀ x4 :
(
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x5 :
(
ι →
(
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x6 .
∀ x7 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
In
(
Inj1
(
setsum
0
(
setsum
0
0
)
)
)
(
Inj1
0
)
⟶
x2
(
λ x8 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x10 .
0
)
(
x7
(
λ x8 :
ι →
ι → ι
.
λ x9 :
ι → ι
.
λ x10 .
x8
(
Inj0
(
setsum
0
0
)
)
(
x9
(
setsum
0
0
)
)
)
)
⟶
x2
(
λ x8 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x10 .
setsum
(
setsum
(
setsum
(
x7
(
λ x11 :
ι →
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
0
)
)
(
setsum
0
0
)
)
(
Inj1
(
setsum
0
0
)
)
)
(
x9
(
λ x11 .
setsum
(
Inj1
0
)
(
x8
(
λ x12 .
λ x13 :
ι → ι
.
0
)
)
)
(
λ x11 .
0
)
)
)
(
x4
(
λ x8 x9 :
ι → ι
.
λ x10 .
x8
0
)
)
)
⟶
(
∀ x4 :
(
ι →
(
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→
ι → ι
.
∀ x5 x6 .
∀ x7 :
ι →
ι → ι
.
x2
(
λ x8 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x10 .
0
)
0
⟶
x3
(
λ x8 :
(
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
0
)
(
λ x8 :
(
ι → ι
)
→ ι
.
0
)
)
⟶
(
∀ x4 :
(
ι →
ι →
ι → ι
)
→ ι
.
∀ x5 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
ι →
ι →
ι → ι
.
∀ x6 x7 .
In
(
Inj0
(
x4
(
λ x8 x9 x10 .
0
)
)
)
(
Inj0
0
)
⟶
x2
(
λ x8 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x10 .
Inj1
x7
)
0
⟶
x1
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 .
Inj1
(
x9
x8
)
)
(
λ x8 :
ι → ι
.
Inj1
(
setsum
(
x8
(
setsum
0
0
)
)
(
Inj0
(
Inj0
0
)
)
)
)
(
λ x8 .
Inj1
(
Inj0
0
)
)
(
λ x8 x9 .
0
)
)
⟶
(
∀ x4 .
∀ x5 :
(
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
∀ x6 x7 .
x1
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 .
Inj0
(
x10
(
λ x12 .
0
)
x8
)
)
(
λ x8 :
ι → ι
.
setsum
x7
(
setsum
(
setsum
0
(
setsum
0
0
)
)
x7
)
)
(
λ x8 .
0
)
(
λ x8 x9 .
0
)
⟶
In
(
Inj1
(
setsum
(
x5
(
λ x8 x9 :
ι → ι
.
λ x10 .
Inj0
0
)
x4
(
λ x8 .
setsum
0
0
)
x7
)
(
Inj0
0
)
)
)
(
setsum
(
setsum
x7
(
setsum
0
(
setsum
0
0
)
)
)
(
setsum
(
setsum
(
setsum
0
0
)
x4
)
x6
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 .
∀ x6 :
ι → ι
.
∀ x7 .
In
x7
(
setsum
0
0
)
⟶
x2
(
λ x8 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x10 .
Inj1
(
setsum
0
(
Inj0
0
)
)
)
(
x6
(
setsum
(
setsum
(
x6
0
)
0
)
(
x6
(
Inj1
0
)
)
)
)
⟶
x0
(
λ x8 :
ι → ι
.
λ x9 .
λ x10 :
ι →
ι → ι
.
Inj1
0
)
(
x6
(
Inj0
(
setsum
(
setsum
0
0
)
0
)
)
)
)
⟶
(
∀ x4 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x5 .
∀ x6 :
(
ι → ι
)
→
ι → ι
.
∀ x7 :
(
ι →
ι →
ι → ι
)
→ ι
.
In
(
Inj0
(
Inj1
0
)
)
x5
⟶
x0
(
λ x8 :
ι → ι
.
λ x9 .
λ x10 :
ι →
ι → ι
.
x8
x9
)
(
x4
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
0
)
)
⟶
x0
(
λ x8 :
ι → ι
.
λ x9 .
λ x10 :
ι →
ι → ι
.
0
)
0
)
⟶
False
)
Known
751ed..
:
not
(
∀ x0 :
(
(
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→ ι
)
→
(
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→ ο
.
∀ x1 :
(
(
(
ι →
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
)
→ ο
.
∀ x2 :
(
ι → ι
)
→
ι → ο
.
∀ x3 :
(
ι → ι
)
→
ι →
ι → ο
.
(
∀ x4 :
ι → ι
.
∀ x5 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
.
∀ x6 x7 :
(
ι →
ι → ι
)
→ ι
.
In
(
setsum
(
setsum
(
setsum
(
x4
0
)
(
setsum
0
0
)
)
(
Inj0
0
)
)
(
setsum
(
x6
(
λ x8 x9 .
Inj1
0
)
)
0
)
)
(
Inj1
(
setsum
(
setsum
(
Inj1
0
)
(
setsum
0
0
)
)
0
)
)
⟶
x3
(
λ x8 .
0
)
0
(
setsum
(
setsum
(
x7
(
λ x8 x9 .
setsum
0
0
)
)
0
)
(
Inj1
(
Inj1
(
Inj0
0
)
)
)
)
⟶
x3
(
λ x8 .
setsum
(
Inj1
(
setsum
(
x7
(
λ x9 x10 .
0
)
)
(
setsum
0
0
)
)
)
(
Inj1
(
setsum
0
(
x5
(
λ x9 :
(
ι → ι
)
→ ι
.
0
)
)
)
)
)
(
x4
(
x7
(
λ x8 x9 .
setsum
0
(
Inj1
0
)
)
)
)
0
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 :
(
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
∀ x6 x7 .
In
(
Inj0
0
)
x7
⟶
x3
(
λ x8 .
Inj0
0
)
0
x6
⟶
x3
(
λ x8 .
0
)
(
setsum
0
0
)
(
Inj0
(
Inj1
0
)
)
)
⟶
(
∀ x4 :
(
(
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
∀ x5 .
∀ x6 :
ι → ι
.
∀ x7 .
x1
(
λ x8 :
(
ι →
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x9 .
0
)
(
λ x8 :
ι →
(
ι → ι
)
→ ι
.
setsum
x7
)
⟶
x2
(
λ x8 .
0
)
(
x4
(
λ x8 x9 :
ι → ι
.
Inj1
(
Inj0
0
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x6 :
ι → ι
.
∀ x7 .
In
(
setsum
x4
(
setsum
(
Inj0
(
setsum
0
0
)
)
(
setsum
0
x7
)
)
)
(
Inj1
0
)
⟶
x2
(
λ x8 .
Inj1
(
Inj1
0
)
)
(
setsum
0
x7
)
⟶
x2
(
λ x8 .
x7
)
(
Inj0
(
Inj1
0
)
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x7 .
In
(
Inj1
(
setsum
(
Inj1
0
)
(
Inj1
(
x6
(
λ x8 :
ι → ι
.
0
)
)
)
)
)
(
Inj0
(
setsum
0
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
)
⟶
x2
(
λ x8 .
Inj0
(
x6
(
λ x9 :
ι → ι
.
setsum
(
Inj0
0
)
0
)
)
)
x5
⟶
x1
(
λ x8 :
(
ι →
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x9 .
Inj0
(
Inj0
(
x6
(
λ x10 :
ι → ι
.
x7
)
)
)
)
(
λ x8 :
ι →
(
ι → ι
)
→ ι
.
λ x9 .
setsum
0
(
setsum
(
setsum
(
Inj1
0
)
x9
)
(
Inj0
x7
)
)
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x5 x6 x7 .
x1
(
λ x8 :
(
ι →
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x9 .
setsum
(
setsum
0
(
setsum
x9
0
)
)
0
)
(
λ x8 :
ι →
(
ι → ι
)
→ ι
.
setsum
0
)
⟶
False
)
⟶
(
∀ x4 :
ι →
ι → ι
.
∀ x5 x6 .
∀ x7 :
ι → ι
.
x0
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
setsum
(
Inj0
0
)
x6
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x9 .
0
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→ ι
.
∀ x5 .
∀ x6 :
(
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→
(
ι →
ι → ι
)
→
ι →
ι → ι
.
∀ x7 .
x0
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
x7
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x9 .
x6
(
λ x10 :
ι →
ι → ι
.
λ x11 x12 .
setsum
0
(
setsum
(
Inj0
0
)
(
setsum
0
0
)
)
)
(
λ x10 x11 .
setsum
x9
(
x8
(
λ x12 :
ι → ι
.
setsum
0
0
)
(
λ x12 .
Inj0
0
)
x9
)
)
x9
(
setsum
(
Inj0
0
)
(
Inj0
(
setsum
0
0
)
)
)
)
⟶
x0
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
setsum
(
x6
(
λ x10 :
ι →
ι → ι
.
λ x11 x12 .
setsum
x12
0
)
(
λ x10 x11 .
x10
)
x7
(
Inj0
(
setsum
0
0
)
)
)
0
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x9 .
setsum
(
setsum
(
setsum
(
setsum
0
0
)
0
)
(
setsum
(
setsum
0
0
)
0
)
)
(
setsum
(
Inj1
(
setsum
0
0
)
)
(
Inj1
(
setsum
0
0
)
)
)
)
)
⟶
False
)
Known
a3378..
:
not
(
∀ x0 :
(
ι → ι
)
→
(
ι → ι
)
→
(
ι → ι
)
→
ι →
ι → ο
.
∀ x1 :
(
(
(
ι →
ι →
ι → ι
)
→
ι → ι
)
→
(
(
ι →
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι →
ι → ι
)
→ ο
.
∀ x2 :
(
(
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι → ι
)
→ ι
)
→ ι
)
→
ι → ο
.
∀ x3 :
(
(
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
)
→ ι
)
→
(
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→
ι → ο
.
(
∀ x4 x5 .
∀ x6 :
ι → ι
.
∀ x7 :
ι →
ι → ι
.
In
(
Inj1
(
setsum
x4
(
Inj0
(
Inj0
0
)
)
)
)
x4
⟶
x0
(
λ x8 .
0
)
(
λ x8 .
Inj1
(
Inj1
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
)
(
λ x8 .
setsum
(
setsum
0
x8
)
(
setsum
(
Inj1
(
Inj0
0
)
)
(
Inj0
0
)
)
)
(
setsum
(
Inj1
(
Inj0
(
Inj1
0
)
)
)
x4
)
0
⟶
x3
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
x5
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
x6
(
Inj1
(
x6
0
)
)
)
x5
(
λ x8 .
x8
)
0
)
⟶
(
∀ x4 x5 .
∀ x6 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x7 .
x3
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
Inj0
0
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
x7
)
(
Inj1
(
setsum
(
Inj1
(
Inj1
0
)
)
(
setsum
(
Inj0
0
)
x5
)
)
)
(
λ x8 .
0
)
(
setsum
(
Inj1
(
Inj0
(
Inj1
0
)
)
)
(
Inj0
x7
)
)
⟶
In
(
Inj0
x4
)
x5
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 :
(
(
ι →
ι → ι
)
→ ι
)
→ ι
.
∀ x6 :
(
ι →
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x7 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
In
(
setsum
(
Inj1
(
Inj0
(
x7
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
0
)
)
)
)
0
)
(
Inj1
(
Inj1
0
)
)
⟶
x2
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
0
)
(
Inj1
0
)
⟶
x2
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
x6
(
λ x9 x10 .
0
)
(
λ x9 :
ι → ι
.
λ x10 .
Inj1
(
Inj0
(
Inj0
0
)
)
)
)
(
Inj1
0
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 x6 .
∀ x7 :
ι →
ι → ι
.
x2
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
0
)
0
⟶
x2
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
x5
)
(
Inj0
x5
)
)
⟶
(
∀ x4 :
(
ι →
ι →
ι → ι
)
→
ι →
(
ι → ι
)
→ ι
.
∀ x5 :
(
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
∀ x6 .
∀ x7 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
.
x3
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
setsum
0
0
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
setsum
(
Inj0
(
setsum
(
Inj1
0
)
(
setsum
0
0
)
)
)
(
setsum
(
x7
(
λ x9 :
(
ι → ι
)
→ ι
.
setsum
0
0
)
)
(
setsum
0
0
)
)
)
(
x5
(
λ x8 .
Inj1
(
setsum
(
Inj0
0
)
(
Inj0
0
)
)
)
(
x7
(
λ x8 :
(
ι → ι
)
→ ι
.
Inj0
(
Inj1
0
)
)
)
(
λ x8 .
0
)
(
Inj0
(
Inj0
(
Inj0
0
)
)
)
)
Inj1
(
setsum
(
Inj1
(
x5
(
λ x8 .
x8
)
(
setsum
0
0
)
(
λ x8 .
0
)
0
)
)
(
Inj1
(
Inj1
(
x7
(
λ x8 :
(
ι → ι
)
→ ι
.
0
)
)
)
)
)
⟶
x1
(
λ x8 :
(
ι →
ι →
ι → ι
)
→
ι → ι
.
λ x9 :
(
ι →
ι → ι
)
→
ι → ι
.
0
)
(
λ x8 x9 x10 .
x9
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
∀ x7 .
x1
(
λ x8 :
(
ι →
ι →
ι → ι
)
→
ι → ι
.
λ x9 :
(
ι →
ι → ι
)
→
ι → ι
.
Inj1
(
setsum
(
setsum
0
0
)
(
Inj0
0
)
)
)
(
λ x8 x9 x10 .
setsum
x9
(
Inj0
(
setsum
x8
x8
)
)
)
⟶
In
(
setsum
(
x6
(
λ x8 .
0
)
(
λ x8 :
ι → ι
.
λ x9 .
Inj0
(
setsum
0
0
)
)
x4
)
(
setsum
0
(
Inj1
0
)
)
)
(
Inj1
x7
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 :
ι →
ι →
(
ι → ι
)
→ ι
.
∀ x6 x7 .
In
(
setsum
(
setsum
0
0
)
0
)
(
x5
0
0
(
λ x8 .
setsum
(
Inj0
(
Inj1
0
)
)
0
)
)
⟶
x0
(
λ x8 .
x6
)
(
λ x8 .
0
)
(
λ x8 .
0
)
x7
x7
⟶
x0
(
λ x8 .
Inj0
0
)
(
λ x8 .
Inj1
0
)
(
λ x8 .
setsum
0
(
x5
0
(
setsum
(
setsum
0
0
)
(
Inj1
0
)
)
(
λ x9 .
x8
)
)
)
0
0
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 :
ι →
ι →
ι →
ι → ι
.
∀ x7 .
In
(
setsum
(
x5
(
Inj1
0
)
)
0
)
(
setsum
(
Inj0
x7
)
(
Inj1
(
setsum
x7
(
setsum
0
0
)
)
)
)
⟶
x0
(
λ x8 .
Inj1
0
)
(
λ x8 .
0
)
(
λ x8 .
Inj1
(
x5
0
)
)
(
x5
(
Inj1
0
)
)
0
⟶
x2
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
setsum
0
(
setsum
(
setsum
0
0
)
(
setsum
(
Inj0
0
)
(
setsum
0
0
)
)
)
)
(
x5
(
setsum
0
x4
)
)
)
⟶
False
)
Known
619f0..
:
not
(
∀ x0 :
(
ι → ι
)
→
(
(
ι →
ι →
ι → ι
)
→ ι
)
→ ο
.
∀ x1 :
(
ι → ι
)
→
(
ι → ι
)
→ ο
.
∀ x2 :
(
(
(
(
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→
ι → ι
)
→
ι →
ι →
ι → ι
)
→
ι → ο
.
∀ x3 :
(
ι → ι
)
→
ι → ο
.
(
∀ x4 x5 x6 x7 .
x3
(
λ x8 .
0
)
0
)
⟶
(
∀ x4 .
∀ x5 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x6 .
∀ x7 :
ι → ι
.
In
(
x7
x4
)
(
Inj0
0
)
⟶
x3
(
λ x8 .
x7
x6
)
(
setsum
(
x7
(
setsum
(
setsum
0
0
)
x6
)
)
0
)
⟶
x2
(
λ x8 :
(
(
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
λ x9 x10 x11 .
setsum
(
x8
(
λ x12 x13 :
ι → ι
.
Inj0
0
)
x10
(
λ x12 .
0
)
(
Inj0
(
setsum
0
0
)
)
)
(
setsum
(
setsum
(
Inj0
0
)
(
Inj0
0
)
)
(
Inj1
x11
)
)
)
(
setsum
(
setsum
(
Inj0
(
setsum
0
0
)
)
(
setsum
(
x5
(
λ x8 :
(
ι → ι
)
→ ι
.
0
)
(
λ x8 :
ι → ι
.
λ x9 .
0
)
)
(
setsum
0
0
)
)
)
(
setsum
(
x5
(
λ x8 :
(
ι → ι
)
→ ι
.
Inj1
0
)
(
λ x8 :
ι → ι
.
λ x9 .
x9
)
)
(
Inj1
(
Inj1
0
)
)
)
)
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
x2
(
λ x8 :
(
(
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
λ x9 x10 x11 .
Inj1
(
Inj0
x9
)
)
(
setsum
(
Inj1
(
Inj0
(
setsum
0
0
)
)
)
(
Inj1
(
setsum
(
Inj0
0
)
0
)
)
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
ι → ι
.
∀ x7 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
In
(
Inj0
(
setsum
(
x7
0
(
λ x8 :
ι → ι
.
λ x9 .
0
)
(
setsum
0
0
)
(
x6
0
)
)
(
x6
(
setsum
0
0
)
)
)
)
(
Inj0
(
Inj1
0
)
)
⟶
x2
(
λ x8 :
(
(
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
λ x9 x10 x11 .
0
)
(
setsum
(
x6
(
Inj1
(
x6
0
)
)
)
(
Inj0
(
x7
(
setsum
0
0
)
(
λ x8 :
ι → ι
.
λ x9 .
0
)
x4
(
x7
0
(
λ x8 :
ι → ι
.
λ x9 .
0
)
0
0
)
)
)
)
⟶
x3
(
λ x8 .
setsum
(
setsum
(
x6
(
Inj1
0
)
)
(
x6
x5
)
)
(
x7
(
setsum
(
Inj0
0
)
(
x7
0
(
λ x9 :
ι → ι
.
λ x10 .
0
)
0
0
)
)
(
λ x9 :
ι → ι
.
λ x10 .
Inj0
0
)
(
Inj0
(
x7
0
(
λ x9 :
ι → ι
.
λ x10 .
0
)
0
0
)
)
(
x7
x8
(
λ x9 :
ι → ι
.
λ x10 .
setsum
0
0
)
0
(
Inj1
0
)
)
)
)
(
Inj0
x4
)
)
⟶
(
∀ x4 :
ι →
(
ι →
ι → ι
)
→
ι →
ι → ι
.
∀ x5 :
(
ι →
ι → ι
)
→ ι
.
∀ x6 .
∀ x7 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
.
In
(
Inj1
(
Inj0
0
)
)
(
setsum
(
x4
(
setsum
(
Inj1
0
)
(
setsum
0
0
)
)
(
λ x8 x9 .
x8
)
(
setsum
(
Inj1
0
)
(
x4
0
(
λ x8 x9 .
0
)
0
0
)
)
x6
)
(
setsum
(
x4
(
Inj1
0
)
(
λ x8 x9 .
Inj1
0
)
(
setsum
0
0
)
0
)
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
)
⟶
x0
(
λ x8 .
Inj1
x6
)
(
λ x8 :
ι →
ι →
ι → ι
.
0
)
⟶
x1
(
λ x8 .
Inj1
(
setsum
0
(
setsum
(
x7
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 .
0
)
)
(
x7
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 .
0
)
)
)
)
)
(
λ x8 .
setsum
(
x5
(
λ x9 x10 .
x10
)
)
(
setsum
0
(
Inj1
0
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x6 :
(
(
ι → ι
)
→
ι →
ι → ι
)
→
ι →
ι → ι
.
∀ x7 :
ι →
(
ι →
ι → ι
)
→ ι
.
In
(
x7
(
setsum
0
0
)
(
λ x8 x9 .
Inj1
(
Inj1
0
)
)
)
(
setsum
(
Inj1
x4
)
(
x6
(
λ x8 :
ι → ι
.
λ x9 x10 .
setsum
x9
0
)
(
setsum
(
setsum
0
0
)
(
x6
(
λ x8 :
ι → ι
.
λ x9 x10 .
0
)
0
0
)
)
(
x6
(
λ x8 :
ι → ι
.
λ x9 x10 .
Inj0
0
)
x4
0
)
)
)
⟶
x1
(
λ x8 .
setsum
0
(
setsum
0
(
Inj1
0
)
)
)
(
λ x8 .
setsum
(
x5
0
(
λ x9 :
ι → ι
.
λ x10 .
0
)
)
(
setsum
(
setsum
0
(
setsum
0
0
)
)
(
Inj0
(
Inj1
0
)
)
)
)
⟶
x1
(
λ x8 .
Inj1
(
x6
(
λ x9 :
ι → ι
.
λ x10 x11 .
setsum
(
Inj1
0
)
(
x9
0
)
)
(
Inj0
(
Inj0
0
)
)
(
Inj0
(
x5
0
(
λ x9 :
ι → ι
.
λ x10 .
0
)
)
)
)
)
(
λ x8 .
0
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
∀ x7 :
ι →
ι →
ι → ι
.
In
x4
(
x7
0
(
Inj1
(
setsum
(
Inj0
0
)
(
Inj0
0
)
)
)
x5
)
⟶
x0
(
λ x8 .
setsum
x8
(
setsum
x8
0
)
)
(
λ x8 :
ι →
ι →
ι → ι
.
0
)
⟶
x0
(
λ x8 .
x7
(
setsum
0
0
)
(
setsum
x8
0
)
(
Inj1
0
)
)
(
λ x8 :
ι →
ι →
ι → ι
.
0
)
)
⟶
(
∀ x4 x5 x6 x7 .
x0
(
λ x8 .
setsum
(
setsum
0
0
)
0
)
(
λ x8 :
ι →
ι →
ι → ι
.
setsum
(
setsum
0
0
)
(
setsum
(
Inj1
0
)
0
)
)
⟶
x3
(
λ x8 .
0
)
(
Inj0
(
setsum
(
Inj0
0
)
(
Inj1
(
setsum
0
0
)
)
)
)
)
⟶
False
)
Theorem
e82b5..
:
(
∀ x0 :
(
(
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
)
→
ι → ο
.
∀ x1 :
(
ι → ι
)
→
(
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
)
→
ι → ο
.
∀ x2 :
(
ι →
ι → ι
)
→
(
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
)
→ ο
.
∀ x3 :
(
ι →
ι → ι
)
→
ι →
ι →
ι → ο
.
(
∀ x4 :
ι →
(
ι →
ι → ι
)
→
ι →
ι → ι
.
∀ x5 x6 x7 .
In
(
setsum
(
x4
(
Inj1
0
)
(
λ x8 x9 .
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
x5
0
)
(
setsum
(
x4
(
Inj0
0
)
(
λ x8 x9 .
0
)
(
setsum
0
0
)
0
)
(
setsum
(
Inj1
0
)
0
)
)
)
(
Inj1
(
setsum
x6
0
)
)
⟶
x0
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→ ι
.
λ x9 :
ι →
ι → ι
.
setsum
0
(
setsum
(
x9
(
Inj1
0
)
(
x9
0
0
)
)
x7
)
)
(
x4
(
setsum
(
x4
(
setsum
0
0
)
(
λ x8 x9 .
setsum
0
0
)
x5
(
setsum
0
0
)
)
x7
)
(
λ x8 x9 .
x9
)
(
setsum
(
Inj1
(
x4
0
(
λ x8 x9 .
0
)
0
0
)
)
(
Inj1
(
Inj1
0
)
)
)
0
)
⟶
x3
(
λ x8 x9 .
x9
)
(
setsum
x5
0
)
(
Inj1
0
)
x6
)
⟶
(
∀ x4 .
∀ x5 :
ι →
(
ι → ι
)
→ ι
.
∀ x6 :
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x7 .
In
(
Inj1
0
)
(
setsum
0
0
)
⟶
x3
(
λ x8 x9 .
0
)
(
setsum
0
(
setsum
0
(
Inj1
0
)
)
)
0
(
Inj1
0
)
⟶
x1
(
λ x8 .
setsum
(
setsum
(
Inj0
(
x5
0
(
λ x9 .
0
)
)
)
x8
)
0
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
Inj1
0
)
(
Inj1
(
setsum
(
Inj1
(
setsum
0
0
)
)
(
x5
0
(
λ x8 .
0
)
)
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
∀ x6 :
(
ι → ι
)
→
ι → ι
.
∀ x7 :
(
ι → ι
)
→ ι
.
In
(
Inj1
(
x4
(
setsum
(
x6
(
λ x8 .
0
)
0
)
(
setsum
0
0
)
)
)
)
(
setsum
(
x4
(
setsum
(
Inj0
0
)
0
)
)
(
x4
0
)
)
⟶
x2
(
λ x8 x9 .
x7
(
λ x10 .
0
)
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x9 x10 .
setsum
(
Inj0
0
)
0
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
∀ x5 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x6 :
ι →
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
∀ x7 .
In
(
setsum
0
(
setsum
(
setsum
(
Inj0
0
)
0
)
(
x5
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
λ x9 :
ι → ι
.
λ x10 .
Inj0
0
)
(
λ x8 x9 .
0
)
(
λ x8 .
x5
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 :
ι → ι
.
λ x11 .
0
)
(
λ x9 x10 .
0
)
(
λ x9 .
0
)
)
)
)
)
(
Inj1
(
x5
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
λ x9 :
ι → ι
.
λ x10 .
setsum
x10
0
)
(
λ x8 x9 .
x8
)
(
λ x8 .
Inj1
(
Inj1
0
)
)
)
)
⟶
x2
(
λ x8 x9 .
0
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x9 x10 .
Inj1
(
Inj0
0
)
)
⟶
x1
(
λ x8 .
Inj1
0
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
setsum
(
setsum
(
setsum
(
setsum
0
0
)
(
Inj1
0
)
)
(
setsum
0
x7
)
)
0
)
(
setsum
(
setsum
(
x4
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 :
ι → ι
.
λ x10 .
0
)
(
x6
0
(
λ x8 :
ι → ι
.
0
)
0
0
)
0
)
(
x4
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 :
ι → ι
.
λ x10 .
0
)
(
setsum
0
0
)
(
setsum
0
0
)
)
)
(
setsum
0
(
x6
x7
(
λ x8 :
ι → ι
.
setsum
0
0
)
(
setsum
0
0
)
(
Inj1
0
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
∀ x6 x7 .
x3
(
λ x8 x9 .
x8
)
0
(
Inj1
0
)
(
setsum
0
0
)
⟶
x1
(
λ x8 .
setsum
(
Inj0
x8
)
(
setsum
0
(
setsum
0
(
setsum
0
0
)
)
)
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
0
)
0
)
⟶
(
∀ x4 :
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x5 :
ι → ι
.
∀ x6 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
∀ x7 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
x1
(
λ x8 .
x7
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 :
ι → ι
.
λ x11 .
setsum
(
Inj1
0
)
0
)
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
Inj1
0
)
(
x5
0
)
⟶
x1
(
λ x8 .
setsum
(
x5
0
)
(
Inj0
0
)
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
Inj0
0
)
(
setsum
(
setsum
0
0
)
(
Inj0
(
setsum
0
(
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 :
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x5 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
∀ x6 :
(
(
ι →
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x7 :
ι → ι
.
x0
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→ ι
.
λ x9 :
ι →
ι → ι
.
x9
0
0
)
(
Inj1
(
setsum
0
(
x6
(
λ x8 :
ι →
ι → ι
.
λ x9 .
Inj0
0
)
(
λ x8 :
ι → ι
.
λ x9 .
x9
)
)
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 :
(
ι → ι
)
→
ι → ι
.
∀ x6 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x7 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
In
(
Inj1
(
setsum
(
x7
(
x4
0
)
(
λ x8 :
ι → ι
.
λ x9 .
setsum
0
0
)
)
0
)
)
(
Inj0
0
)
⟶
x0
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→ ι
.
λ x9 :
ι →
ι → ι
.
setsum
0
(
x7
(
x6
(
setsum
0
0
)
(
λ x10 :
ι → ι
.
λ x11 .
Inj1
0
)
(
λ x10 .
setsum
0
0
)
)
(
λ x10 :
ι → ι
.
λ x11 .
setsum
(
x10
0
)
0
)
)
)
(
Inj1
(
setsum
(
x4
(
Inj1
0
)
)
(
Inj0
0
)
)
)
⟶
x3
(
λ x8 x9 .
setsum
(
setsum
(
x6
(
setsum
0
0
)
(
λ x10 :
ι → ι
.
λ x11 .
setsum
0
0
)
(
λ x10 .
x10
)
)
(
Inj1
0
)
)
(
Inj0
0
)
)
0
0
(
x7
0
(
λ x8 :
ι → ι
.
λ x9 .
x9
)
)
)
⟶
False
)
⟶
∀ x0 : ο .
x0
(proof)
Theorem
6da2e..
:
(
∀ x0 :
(
(
(
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→ ι
)
→ ι
)
→
(
ι →
ι →
ι → ι
)
→ ο
.
∀ x1 :
(
(
(
ι →
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι →
(
(
ι → ι
)
→
ι → ι
)
→
ι → ο
.
∀ x2 :
(
ι →
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
)
→
ι →
ι →
(
ι → ι
)
→
ι → ο
.
∀ x3 :
(
ι → ι
)
→
(
(
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ο
.
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 .
∀ x7 :
ι → ι
.
In
(
Inj1
(
setsum
(
setsum
(
Inj0
0
)
(
x5
0
)
)
(
x5
0
)
)
)
(
Inj1
(
Inj0
(
x5
(
x7
0
)
)
)
)
⟶
x3
(
λ x8 .
setsum
(
setsum
(
Inj0
(
Inj1
0
)
)
(
Inj1
(
setsum
0
0
)
)
)
x6
)
(
λ x8 :
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
λ x9 :
(
ι → ι
)
→ ι
.
setsum
0
(
x8
(
λ x10 :
ι → ι
.
λ x11 .
setsum
(
setsum
0
0
)
0
)
(
x7
(
x7
0
)
)
)
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
(
ι →
ι →
ι → ι
)
→
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x7 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
x3
(
λ x8 .
Inj0
(
setsum
(
setsum
(
Inj0
0
)
x8
)
(
x6
(
λ x9 x10 x11 .
x11
)
(
λ x9 .
0
)
(
λ x9 .
0
)
(
Inj0
0
)
)
)
)
(
λ x8 :
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
λ x9 :
(
ι → ι
)
→ ι
.
x8
(
λ x10 :
ι → ι
.
λ x11 .
x10
(
Inj1
0
)
)
(
Inj0
0
)
)
⟶
x1
(
λ x8 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
λ x9 .
x9
)
(
λ x8 .
setsum
(
setsum
0
0
)
0
)
x4
(
λ x8 :
ι → ι
.
λ x9 .
0
)
0
)
⟶
(
∀ x4 :
(
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
∀ x5 :
ι →
ι →
(
ι → ι
)
→ ι
.
∀ x6 :
(
ι → ι
)
→
(
ι → ι
)
→
ι →
ι → ι
.
∀ x7 .
x3
(
λ x8 .
setsum
(
Inj1
0
)
(
Inj1
(
x5
0
(
setsum
0
0
)
(
λ x9 .
x6
(
λ x10 .
0
)
(
λ x10 .
0
)
0
0
)
)
)
)
(
λ x8 :
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
λ x9 :
(
ι → ι
)
→ ι
.
Inj1
(
x9
(
λ x10 .
x8
(
λ x11 :
ι → ι
.
λ x12 .
Inj1
0
)
(
x8
(
λ x11 :
ι → ι
.
λ x12 .
0
)
0
)
)
)
)
⟶
x2
(
λ x8 .
λ x9 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
0
)
0
(
Inj0
(
setsum
(
Inj1
(
x5
0
0
(
λ x8 .
0
)
)
)
(
x4
(
λ x8 :
ι →
ι → ι
.
λ x9 x10 .
Inj0
0
)
)
)
)
(
λ x8 .
0
)
0
)
⟶
(
∀ x4 :
ι →
(
ι → ι
)
→
ι →
ι → ι
.
∀ x5 :
(
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι →
ι →
ι → ι
.
∀ x6 :
ι →
(
ι →
ι → ι
)
→
ι →
ι → ι
.
∀ x7 .
In
x7
(
Inj0
(
x5
(
λ x8 x9 :
ι → ι
.
λ x10 .
Inj1
(
setsum
0
0
)
)
(
Inj0
0
)
(
x6
0
(
λ x8 x9 .
setsum
0
0
)
(
x4
0
(
λ x8 .
0
)
0
0
)
0
)
x7
)
)
⟶
x2
(
λ x8 .
λ x9 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
setsum
(
setsum
x8
(
x9
(
λ x10 x11 .
Inj1
0
)
(
λ x10 .
setsum
0
0
)
)
)
(
setsum
x8
(
Inj0
(
x9
(
λ x10 x11 .
0
)
(
λ x10 .
0
)
)
)
)
)
0
0
(
setsum
(
x5
(
λ x8 x9 :
ι → ι
.
λ x10 .
Inj0
(
x9
0
)
)
(
x6
(
Inj1
0
)
(
λ x8 x9 .
setsum
0
0
)
(
setsum
0
0
)
(
Inj1
0
)
)
(
Inj1
(
setsum
0
0
)
)
(
setsum
(
Inj1
0
)
0
)
)
)
0
⟶
x0
(
λ x8 :
(
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
setsum
0
(
Inj0
(
setsum
(
Inj0
0
)
(
setsum
0
0
)
)
)
)
(
λ x8 x9 x10 .
x7
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
∀ x6 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι → ι
.
∀ x7 :
ι → ι
.
In
(
Inj0
(
setsum
(
Inj1
(
x7
0
)
)
0
)
)
(
setsum
(
setsum
0
(
setsum
(
Inj0
0
)
(
x5
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
0
)
)
)
)
(
Inj1
(
Inj1
0
)
)
)
⟶
x0
(
λ x8 :
(
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
Inj1
(
Inj0
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
)
(
λ x8 x9 x10 .
x8
)
⟶
x1
(
λ x8 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
x8
(
λ x9 .
λ x10 :
ι → ι
.
0
)
(
x7
0
)
)
(
λ x8 .
0
)
0
(
λ x8 :
ι → ι
.
λ x9 .
x7
(
Inj0
(
Inj1
(
x6
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
0
)
0
)
)
)
)
(
setsum
(
Inj1
0
)
(
setsum
(
Inj1
(
Inj0
0
)
)
(
setsum
(
x7
0
)
(
Inj0
0
)
)
)
)
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
ι →
ι →
ι → ι
.
In
x5
(
setsum
x6
(
setsum
0
0
)
)
⟶
x1
(
λ x8 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
λ x9 .
x9
)
(
λ x8 .
Inj1
(
Inj1
x8
)
)
0
(
λ x8 :
ι → ι
.
λ x9 .
Inj0
(
x8
x9
)
)
x5
⟶
x3
(
λ x8 .
Inj1
(
setsum
x6
(
setsum
0
x8
)
)
)
(
λ x8 :
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
λ x9 :
(
ι → ι
)
→ ι
.
Inj0
(
setsum
(
Inj1
(
x9
(
λ x10 .
0
)
)
)
(
x7
(
x7
0
0
0
)
(
Inj1
0
)
(
Inj1
0
)
)
)
)
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
ι → ι
.
x0
(
λ x8 :
(
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
setsum
x6
(
Inj1
(
setsum
(
Inj1
0
)
(
setsum
0
0
)
)
)
)
(
λ x8 x9 x10 .
Inj1
(
Inj0
0
)
)
⟶
x0
(
λ x8 :
(
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
0
)
(
λ x8 x9 x10 .
Inj1
(
Inj1
(
Inj1
(
Inj1
0
)
)
)
)
)
⟶
(
∀ x4 :
ι →
ι →
(
ι → ι
)
→ ι
.
∀ x5 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
∀ x6 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
∀ x7 .
x0
(
λ x8 :
(
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
x6
0
0
(
λ x9 .
0
)
0
)
(
λ x8 x9 x10 .
0
)
⟶
x0
(
λ x8 :
(
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
x6
(
x8
(
λ x9 :
ι →
ι → ι
.
λ x10 x11 .
x9
(
x8
(
λ x12 :
ι →
ι → ι
.
λ x13 x14 .
0
)
)
(
setsum
0
0
)
)
)
(
setsum
0
(
setsum
(
Inj0
0
)
0
)
)
(
λ x9 .
setsum
0
(
setsum
(
x6
0
0
(
λ x10 .
0
)
0
)
0
)
)
(
setsum
(
Inj1
(
setsum
0
0
)
)
(
x8
(
λ x9 :
ι →
ι → ι
.
λ x10 x11 .
0
)
)
)
)
(
λ x8 x9 x10 .
x10
)
)
⟶
False
)
⟶
∀ x0 : ο .
x0
(proof)
Theorem
436a3..
:
(
∀ x0 :
(
(
ι →
ι →
ι → ι
)
→
ι →
ι → ι
)
→
ι → ο
.
∀ x1 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ο
.
∀ x2 :
(
ι → ι
)
→
ι → ο
.
∀ x3 :
(
ι →
ι →
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
)
→ ο
.
(
∀ x4 :
ι →
ι → ι
.
∀ x5 .
∀ x6 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
∀ x7 :
(
ι →
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
In
(
setsum
0
(
x7
(
λ x8 .
λ x9 :
ι → ι
.
x7
(
λ x10 .
λ x11 :
ι → ι
.
0
)
(
λ x10 .
setsum
0
0
)
0
)
(
λ x8 .
0
)
(
Inj1
(
x6
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
0
)
)
)
)
)
(
setsum
(
x7
(
λ x8 .
λ x9 :
ι → ι
.
x7
(
λ x10 .
λ x11 :
ι → ι
.
0
)
(
λ x10 .
Inj1
0
)
(
x6
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
0
)
)
)
(
λ x8 .
Inj1
(
setsum
0
0
)
)
0
)
(
setsum
(
x6
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
0
)
)
(
setsum
(
setsum
0
0
)
(
Inj1
0
)
)
)
)
⟶
x3
(
λ x8 x9 x10 x11 x12 .
Inj0
0
)
(
λ x8 :
ι → ι
.
λ x9 :
ι →
ι → ι
.
x8
(
x6
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
0
)
)
)
)
⟶
(
∀ x4 :
ι →
(
ι →
ι → ι
)
→
ι →
ι → ι
.
∀ x5 :
(
ι →
ι →
ι → ι
)
→
ι →
ι → ι
.
∀ x6 .
∀ x7 :
(
ι → ι
)
→ ι
.
In
(
Inj1
(
setsum
(
x5
(
λ x8 x9 x10 .
Inj0
0
)
(
setsum
0
0
)
(
setsum
0
0
)
)
(
setsum
x6
(
x7
(
λ x8 .
0
)
)
)
)
)
x6
⟶
x3
(
λ x8 x9 x10 x11 x12 .
Inj1
(
setsum
(
Inj1
0
)
x12
)
)
(
λ x8 :
ι → ι
.
λ x9 :
ι →
ι → ι
.
Inj1
(
Inj1
(
Inj0
(
Inj1
0
)
)
)
)
⟶
x3
(
λ x8 x9 x10 x11 x12 .
Inj1
(
setsum
0
(
setsum
(
Inj0
0
)
0
)
)
)
(
λ x8 :
ι → ι
.
λ x9 :
ι →
ι → ι
.
Inj0
(
Inj0
(
x9
(
x7
(
λ x10 .
0
)
)
(
x7
(
λ x10 .
0
)
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
(
ι → ι
)
→ ι
.
∀ x6 x7 .
In
(
Inj0
x7
)
(
setsum
0
0
)
⟶
x2
(
λ x8 .
0
)
x6
⟶
x2
(
λ x8 .
0
)
(
Inj1
0
)
)
⟶
(
∀ x4 x5 x6 x7 .
x2
(
λ x8 .
x6
)
x4
⟶
In
x5
(
Inj1
0
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→
ι → ι
.
∀ x5 :
(
(
ι →
ι → ι
)
→ ι
)
→ ι
.
∀ x6 .
∀ x7 :
ι → ι
.
In
(
x5
(
λ x8 :
ι →
ι → ι
.
0
)
)
(
x5
(
λ x8 :
ι →
ι → ι
.
Inj0
(
x8
(
Inj1
0
)
(
setsum
0
0
)
)
)
)
⟶
x1
(
λ x8 :
ι → ι
.
Inj0
0
)
(
λ x8 .
0
)
(
x5
(
λ x8 :
ι →
ι → ι
.
0
)
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
(
ι → ι
)
→
ι → ι
.
∀ x7 .
x1
(
λ x8 :
ι → ι
.
x6
(
λ x9 .
x7
)
(
Inj1
(
Inj0
(
Inj1
0
)
)
)
)
(
λ x8 .
setsum
(
x6
(
λ x9 .
setsum
x9
0
)
(
Inj1
(
Inj1
0
)
)
)
0
)
(
setsum
0
(
Inj1
0
)
)
⟶
x0
(
λ x8 :
ι →
ι →
ι → ι
.
λ x9 x10 .
setsum
x7
(
setsum
x10
(
x8
(
setsum
0
0
)
0
(
setsum
0
0
)
)
)
)
0
)
⟶
(
∀ x4 x5 .
∀ x6 :
ι → ι
.
∀ x7 .
x0
(
λ x8 :
ι →
ι →
ι → ι
.
λ x9 x10 .
0
)
0
⟶
x0
(
λ x8 :
ι →
ι →
ι → ι
.
λ x9 x10 .
0
)
(
Inj1
x7
)
)
⟶
(
∀ x4 x5 x6 x7 .
x0
(
λ x8 :
ι →
ι →
ι → ι
.
λ x9 x10 .
x10
)
(
Inj0
0
)
⟶
x3
(
λ x8 x9 x10 x11 x12 .
Inj1
0
)
(
λ x8 :
ι → ι
.
λ x9 :
ι →
ι → ι
.
0
)
)
⟶
False
)
⟶
∀ x0 : ο .
x0
(proof)
Theorem
08f46..
:
(
∀ x0 :
(
(
(
ι → ι
)
→
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι →
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ο
.
∀ x1 :
(
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ο
.
∀ x2 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ο
.
∀ x3 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
(
ι →
ι → ι
)
→ ι
)
→
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι → ο
.
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x7 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
In
(
Inj1
(
x5
0
)
)
(
Inj0
(
Inj1
(
Inj1
(
setsum
0
0
)
)
)
)
⟶
x2
(
λ x8 .
x7
(
λ x9 .
setsum
(
setsum
(
setsum
0
0
)
0
)
(
x6
(
λ x10 .
λ x11 :
ι → ι
.
λ x12 .
Inj1
0
)
)
)
(
λ x9 :
ι → ι
.
λ x10 .
setsum
0
(
x7
(
λ x11 .
Inj0
0
)
(
λ x11 :
ι → ι
.
λ x12 .
0
)
)
)
)
(
λ x8 x9 .
0
)
⟶
x3
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 .
setsum
(
x8
(
λ x10 .
setsum
(
setsum
0
0
)
(
Inj0
0
)
)
)
0
)
(
λ x8 :
ι →
ι → ι
.
Inj0
0
)
(
λ x8 :
(
ι → ι
)
→ ι
.
0
)
(
Inj1
0
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 x6 .
∀ x7 :
ι → ι
.
x3
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 .
setsum
(
x7
(
setsum
x9
(
Inj1
0
)
)
)
(
Inj0
(
setsum
0
(
Inj1
0
)
)
)
)
(
λ x8 :
ι →
ι → ι
.
0
)
(
λ x8 :
(
ι → ι
)
→ ι
.
setsum
x6
(
setsum
(
x8
(
λ x9 .
Inj0
0
)
)
(
x7
0
)
)
)
(
setsum
(
setsum
(
x7
0
)
x5
)
(
Inj1
(
setsum
(
Inj1
0
)
(
setsum
0
0
)
)
)
)
⟶
In
(
Inj0
0
)
(
Inj1
0
)
)
⟶
(
∀ x4 x5 x6 x7 .
In
(
Inj1
x7
)
(
Inj0
(
Inj0
x5
)
)
⟶
x3
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 .
Inj0
(
setsum
(
setsum
(
Inj0
0
)
0
)
(
setsum
0
(
x8
(
λ x10 .
0
)
)
)
)
)
(
λ x8 :
ι →
ι → ι
.
0
)
(
λ x8 :
(
ι → ι
)
→ ι
.
x6
)
(
Inj0
0
)
⟶
x2
(
λ x8 .
Inj0
x6
)
(
λ x8 x9 .
setsum
(
setsum
0
0
)
x6
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
∀ x5 x6 .
∀ x7 :
ι → ι
.
x2
(
λ x8 .
0
)
(
λ x8 x9 .
0
)
⟶
In
(
Inj0
x6
)
(
setsum
x6
(
Inj1
(
Inj0
(
Inj0
0
)
)
)
)
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
ι → ι
.
In
(
Inj0
0
)
(
Inj1
(
setsum
x6
0
)
)
⟶
x2
(
λ x8 .
Inj0
0
)
(
λ x8 x9 .
setsum
(
x7
(
setsum
0
0
)
)
0
)
⟶
x1
(
λ x8 x9 .
0
)
(
λ x8 :
ι → ι
.
x6
)
)
⟶
(
∀ x4 x5 x6 x7 .
x1
(
λ x8 x9 .
setsum
(
setsum
0
(
setsum
(
Inj1
0
)
x7
)
)
(
Inj1
(
setsum
x6
x6
)
)
)
(
λ x8 :
ι → ι
.
0
)
⟶
x1
(
λ x8 x9 .
x6
)
(
λ x8 :
ι → ι
.
x7
)
)
⟶
(
∀ x4 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
∀ x5 :
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
∀ x6 .
∀ x7 :
ι →
ι → ι
.
x2
(
λ x8 .
0
)
(
λ x8 x9 .
Inj1
0
)
⟶
x0
(
λ x8 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
(
ι → ι
)
→
ι → ι
.
0
)
(
x7
(
setsum
(
Inj0
(
setsum
0
0
)
)
(
setsum
(
setsum
0
0
)
(
Inj0
0
)
)
)
(
Inj1
(
setsum
0
(
setsum
0
0
)
)
)
)
(
setsum
0
(
setsum
(
x4
(
setsum
0
0
)
0
(
λ x8 .
setsum
0
0
)
(
setsum
0
0
)
)
(
setsum
(
x7
0
0
)
(
Inj1
0
)
)
)
)
(
λ x8 :
ι → ι
.
λ x9 .
setsum
x9
(
Inj0
x9
)
)
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
ι → ι
.
x0
(
λ x8 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
(
ι → ι
)
→
ι → ι
.
0
)
x6
x5
(
λ x8 :
ι → ι
.
λ x9 .
setsum
(
Inj1
(
setsum
(
Inj1
0
)
x9
)
)
(
Inj0
x9
)
)
⟶
x2
(
λ x8 .
Inj0
(
x7
0
)
)
(
λ x8 x9 .
x6
)
)
⟶
False
)
⟶
∀ x0 : ο .
x0
(proof)
Theorem
4f3f6..
:
(
∀ x0 :
(
ι → ι
)
→
ι → ο
.
∀ x1 :
(
ι →
(
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
)
→
(
(
ι →
(
ι → ι
)
→ ι
)
→ ι
)
→ ο
.
∀ x2 :
(
ι → ι
)
→
ι →
ι →
ι → ο
.
∀ x3 :
(
(
(
ι →
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι →
ι → ι
)
→
ι → ι
)
→
ι → ο
.
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 :
(
ι → ι
)
→ ι
.
∀ x7 :
ι → ι
.
In
(
Inj1
(
setsum
(
Inj0
(
setsum
0
0
)
)
x4
)
)
(
Inj1
(
x7
(
setsum
0
(
setsum
0
0
)
)
)
)
⟶
x1
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
λ x12 .
x12
)
(
λ x8 :
ι →
(
ι → ι
)
→ ι
.
x5
0
)
⟶
x3
(
λ x8 :
(
ι →
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x9 .
λ x10 :
ι →
ι → ι
.
λ x11 .
Inj1
(
Inj1
(
setsum
(
setsum
0
0
)
(
Inj0
0
)
)
)
)
(
x5
(
setsum
(
Inj1
(
Inj1
0
)
)
0
)
)
)
⟶
(
∀ x4 :
ι →
(
ι →
ι → ι
)
→
ι → ι
.
∀ x5 x6 x7 .
x3
(
λ x8 :
(
ι →
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x9 .
λ x10 :
ι →
ι → ι
.
λ x11 .
setsum
(
x8
(
λ x12 x13 x14 .
Inj1
(
Inj1
0
)
)
(
λ x12 .
Inj0
0
)
(
x10
(
x10
0
0
)
0
)
)
(
Inj1
0
)
)
x7
⟶
x3
(
λ x8 :
(
ι →
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x9 .
λ x10 :
ι →
ι → ι
.
λ x11 .
0
)
x7
)
⟶
(
∀ x4 .
∀ x5 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x6 :
ι → ι
.
∀ x7 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
x2
(
λ x8 .
x7
(
λ x9 :
ι → ι
.
0
)
(
Inj0
(
setsum
0
0
)
)
)
0
(
Inj1
0
)
(
Inj0
(
setsum
(
x5
(
Inj1
0
)
(
λ x8 :
ι → ι
.
x7
(
λ x9 :
ι → ι
.
0
)
0
)
)
(
x6
x4
)
)
)
⟶
x2
(
λ x8 .
Inj0
0
)
(
setsum
x4
(
Inj0
(
x5
0
(
λ x8 :
ι → ι
.
setsum
0
0
)
)
)
)
x4
0
)
⟶
(
∀ x4 x5 x6 x7 .
x2
(
λ x8 .
0
)
(
Inj0
(
Inj1
x4
)
)
(
Inj0
(
setsum
(
Inj0
0
)
0
)
)
(
setsum
(
setsum
x4
0
)
0
)
⟶
In
x7
(
Inj1
0
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
∀ x6 .
∀ x7 :
(
ι →
ι → ι
)
→
ι →
ι → ι
.
x3
(
λ x8 :
(
ι →
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x9 .
λ x10 :
ι →
ι → ι
.
λ x11 .
setsum
0
(
Inj0
(
Inj1
(
x10
0
0
)
)
)
)
(
Inj1
0
)
⟶
x1
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
λ x12 .
x12
)
(
λ x8 :
ι →
(
ι → ι
)
→ ι
.
x5
0
(
setsum
(
Inj0
(
setsum
0
0
)
)
0
)
(
λ x9 .
x6
)
(
x8
(
setsum
(
Inj1
0
)
0
)
(
λ x9 .
0
)
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 .
∀ x6 :
(
ι → ι
)
→
ι →
ι → ι
.
∀ x7 .
x1
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
λ x12 .
0
)
(
λ x8 :
ι →
(
ι → ι
)
→ ι
.
0
)
⟶
False
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 :
(
ι →
ι →
ι → ι
)
→ ι
.
∀ x7 .
In
(
Inj1
(
Inj0
(
setsum
0
(
x6
(
λ x8 x9 x10 .
0
)
)
)
)
)
(
Inj0
(
setsum
x4
0
)
)
⟶
x3
(
λ x8 :
(
ι →
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x9 .
λ x10 :
ι →
ι → ι
.
λ x11 .
0
)
x7
⟶
x0
(
λ x8 .
Inj0
(
Inj0
(
setsum
(
x5
0
)
(
Inj1
0
)
)
)
)
(
Inj1
0
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x7 .
In
(
Inj1
0
)
x4
⟶
x0
(
λ x8 .
setsum
0
(
Inj0
(
x6
(
λ x9 :
ι → ι
.
λ x10 .
0
)
)
)
)
(
setsum
x7
x7
)
⟶
x3
(
λ x8 :
(
ι →
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x9 .
λ x10 :
ι →
ι → ι
.
λ x11 .
0
)
(
Inj1
(
Inj1
x5
)
)
)
⟶
False
)
⟶
∀ x0 : ο .
x0
(proof)
Theorem
db1af..
:
(
∀ x0 :
(
ι →
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι →
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ο
.
∀ x1 :
(
(
(
(
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→
ι → ο
.
∀ x2 :
(
ι →
(
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
)
→ ι
)
→
ι → ο
.
∀ x3 :
(
ι → ι
)
→
(
(
ι →
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→ ι
)
→ ο
.
(
∀ x4 x5 .
∀ x6 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
.
∀ x7 :
ι →
ι → ι
.
In
(
Inj1
(
Inj1
x4
)
)
x4
⟶
x0
(
λ x8 .
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
0
)
(
setsum
(
x7
0
x4
)
(
Inj0
(
setsum
(
Inj0
0
)
0
)
)
)
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
setsum
(
Inj0
(
setsum
x5
x5
)
)
(
Inj1
0
)
)
⟶
x3
(
λ x8 .
x6
(
λ x9 :
(
ι → ι
)
→ ι
.
setsum
(
Inj1
(
setsum
0
0
)
)
(
x7
(
Inj1
0
)
0
)
)
)
(
λ x8 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x9 .
λ x10 :
ι → ι
.
0
)
)
⟶
(
∀ x4 .
∀ x5 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→ ι
.
∀ x6 x7 .
x3
(
λ x8 .
0
)
(
λ x8 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x9 .
λ x10 :
ι → ι
.
setsum
(
Inj1
(
setsum
x7
(
Inj1
0
)
)
)
0
)
⟶
False
)
⟶
(
∀ x4 :
ι →
ι → ι
.
∀ x5 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
.
∀ x6 x7 .
x1
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→ ι
.
λ x9 x10 .
0
)
(
setsum
(
setsum
(
x5
(
λ x8 :
(
ι → ι
)
→ ι
.
setsum
0
0
)
)
(
Inj0
(
Inj1
0
)
)
)
(
x4
(
Inj1
(
setsum
0
0
)
)
(
Inj0
0
)
)
)
⟶
x2
(
λ x8 .
λ x9 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
Inj0
x8
)
(
Inj1
(
setsum
x7
(
setsum
0
(
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
(
ι →
ι → ι
)
→ ι
.
∀ x6 .
∀ x7 :
(
(
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
x2
(
λ x8 .
λ x9 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
Inj0
(
setsum
(
Inj1
(
setsum
0
0
)
)
x6
)
)
(
Inj0
(
Inj0
(
Inj1
(
Inj1
0
)
)
)
)
⟶
x1
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→ ι
.
λ x9 x10 .
0
)
0
)
⟶
(
∀ x4 .
∀ x5 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x6 x7 :
ι → ι
.
In
(
setsum
0
(
setsum
(
setsum
(
x5
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
0
)
)
(
setsum
0
0
)
)
(
Inj1
(
Inj0
0
)
)
)
)
(
Inj0
(
setsum
(
Inj0
(
Inj0
0
)
)
0
)
)
⟶
x3
(
λ x8 .
setsum
0
(
Inj0
(
Inj1
(
Inj0
0
)
)
)
)
(
λ x8 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x9 .
λ x10 :
ι → ι
.
0
)
⟶
x1
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→ ι
.
λ x9 x10 .
setsum
(
Inj1
0
)
(
Inj1
0
)
)
(
setsum
0
(
setsum
0
0
)
)
)
⟶
(
∀ x4 :
(
ι →
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
∀ x5 :
ι →
(
ι →
ι → ι
)
→ ι
.
∀ x6 .
∀ x7 :
ι → ι
.
x1
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→ ι
.
λ x9 x10 .
0
)
(
setsum
(
x7
(
x5
0
(
λ x8 x9 .
0
)
)
)
(
setsum
x6
x6
)
)
⟶
In
(
Inj1
(
setsum
(
Inj0
(
setsum
0
0
)
)
(
setsum
(
Inj1
0
)
(
setsum
0
0
)
)
)
)
(
x4
(
λ x8 x9 .
setsum
(
setsum
x6
0
)
(
Inj0
(
x7
0
)
)
)
(
setsum
0
0
)
(
λ x8 .
0
)
(
setsum
(
x7
(
setsum
0
0
)
)
(
Inj1
(
Inj0
0
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
ι → ι
.
∀ x6 :
ι → ι
.
∀ x7 .
x3
(
λ x8 .
x7
)
(
λ x8 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x9 .
λ x10 :
ι → ι
.
setsum
0
(
Inj0
(
setsum
(
x8
0
(
λ x11 .
0
)
0
)
0
)
)
)
⟶
x0
(
λ x8 .
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
x8
)
(
setsum
(
setsum
(
Inj0
0
)
x4
)
0
)
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
Inj1
(
setsum
0
(
x6
(
x5
0
0
)
)
)
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
(
(
ι → ι
)
→
ι →
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x7 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
x0
(
λ x8 .
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
Inj0
0
)
(
setsum
0
(
x7
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
setsum
(
x7
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
0
)
)
(
Inj1
0
)
)
)
)
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
x5
)
⟶
False
)
⟶
False
)
⟶
∀ x0 : ο .
x0
(proof)
Theorem
e07c2..
:
(
∀ x0 :
(
ι → ι
)
→
ι →
ι → ο
.
∀ x1 :
(
(
ι → ι
)
→ ι
)
→
(
(
ι →
ι →
ι → ι
)
→ ι
)
→
(
ι →
ι →
ι → ι
)
→ ο
.
∀ x2 :
(
ι → ι
)
→
(
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
)
→
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ο
.
∀ x3 :
(
(
ι →
(
ι → ι
)
→ ι
)
→
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
)
→
(
(
ι →
ι →
ι → ι
)
→ ι
)
→
(
ι →
ι →
ι → ι
)
→
ι → ο
.
(
∀ x4 :
ι →
(
ι →
ι → ι
)
→ ι
.
∀ x5 .
∀ x6 :
ι →
ι → ι
.
∀ x7 .
x0
(
λ x8 .
0
)
(
setsum
0
(
Inj1
(
setsum
x7
(
setsum
0
0
)
)
)
)
(
setsum
(
x4
(
x6
(
Inj0
0
)
(
setsum
0
0
)
)
(
λ x8 x9 .
x9
)
)
(
setsum
0
x7
)
)
⟶
x3
(
λ x8 :
ι →
(
ι → ι
)
→ ι
.
λ x9 :
(
(
ι → ι
)
→ ι
)
→ ι
.
0
)
(
λ x8 :
ι →
ι →
ι → ι
.
0
)
(
λ x8 x9 x10 .
setsum
(
Inj1
(
Inj0
(
Inj1
0
)
)
)
(
Inj0
0
)
)
(
setsum
(
Inj0
(
setsum
(
Inj1
0
)
(
Inj1
0
)
)
)
0
)
)
⟶
(
∀ x4 :
(
(
ι →
ι → ι
)
→ ι
)
→ ι
.
∀ x5 :
ι → ι
.
∀ x6 x7 .
In
x7
(
Inj1
(
Inj1
(
Inj0
x6
)
)
)
⟶
x3
(
λ x8 :
ι →
(
ι → ι
)
→ ι
.
λ x9 :
(
(
ι → ι
)
→ ι
)
→ ι
.
0
)
(
λ x8 :
ι →
ι →
ι → ι
.
setsum
(
Inj1
(
Inj1
(
setsum
0
0
)
)
)
0
)
(
λ x8 x9 x10 .
setsum
0
(
Inj0
(
Inj1
(
Inj0
0
)
)
)
)
0
⟶
x3
(
λ x8 :
ι →
(
ι → ι
)
→ ι
.
λ x9 :
(
(
ι → ι
)
→ ι
)
→ ι
.
Inj1
(
setsum
(
Inj1
(
x8
0
(
λ x10 .
0
)
)
)
0
)
)
(
λ x8 :
ι →
ι →
ι → ι
.
setsum
(
Inj1
0
)
(
setsum
0
0
)
)
(
λ x8 x9 x10 .
x9
)
(
x4
(
λ x8 :
ι →
ι → ι
.
setsum
x7
(
setsum
(
Inj0
0
)
(
x8
0
0
)
)
)
)
)
⟶
(
∀ x4 x5 x6 x7 .
x2
(
λ x8 .
setsum
(
Inj1
0
)
(
Inj1
0
)
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 x11 .
x9
(
λ x12 .
Inj0
(
Inj0
(
setsum
0
0
)
)
)
0
)
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 x10 .
Inj0
(
Inj1
0
)
)
(
Inj1
(
Inj0
(
setsum
0
0
)
)
)
(
λ x8 .
setsum
(
Inj1
0
)
(
setsum
0
(
setsum
(
Inj0
0
)
x5
)
)
)
0
⟶
x2
(
λ x8 .
setsum
0
0
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 x11 .
setsum
(
setsum
x10
0
)
(
setsum
(
Inj1
(
Inj1
0
)
)
(
setsum
(
x8
(
λ x12 :
ι → ι
.
0
)
)
x10
)
)
)
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 x10 .
Inj1
(
x8
(
λ x11 .
setsum
(
setsum
0
0
)
(
Inj0
0
)
)
)
)
(
setsum
(
Inj1
(
Inj0
x6
)
)
(
Inj1
(
setsum
0
(
Inj1
0
)
)
)
)
(
λ x8 .
Inj1
(
Inj0
(
setsum
(
Inj0
0
)
(
Inj0
0
)
)
)
)
(
setsum
x7
(
Inj1
0
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 x6 x7 .
In
x7
(
Inj0
0
)
⟶
x2
(
λ x8 .
0
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 x11 .
x10
)
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 x10 .
0
)
(
Inj1
(
setsum
x7
(
setsum
(
Inj0
0
)
0
)
)
)
(
λ x8 .
x8
)
(
setsum
(
Inj1
(
x4
(
Inj0
0
)
)
)
(
Inj1
x7
)
)
⟶
x2
Inj0
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 x11 .
x8
(
λ x12 :
ι → ι
.
0
)
)
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 x10 .
setsum
x7
0
)
(
setsum
(
setsum
0
0
)
0
)
(
λ x8 .
Inj0
(
Inj0
x5
)
)
0
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 .
∀ x6 :
ι → ι
.
∀ x7 :
(
ι →
ι →
ι → ι
)
→ ι
.
In
(
setsum
(
Inj0
(
Inj0
(
Inj1
0
)
)
)
(
setsum
0
x5
)
)
(
x4
(
setsum
(
setsum
x5
(
setsum
0
0
)
)
(
Inj1
x5
)
)
)
⟶
x2
(
λ x8 .
setsum
(
x7
(
λ x9 x10 x11 .
0
)
)
x5
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 x11 .
0
)
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 x10 .
x8
(
λ x11 .
setsum
x10
0
)
)
(
setsum
0
(
setsum
(
Inj1
0
)
(
Inj0
x5
)
)
)
(
λ x8 .
x7
(
λ x9 x10 x11 .
setsum
(
setsum
(
setsum
0
0
)
(
Inj1
0
)
)
(
Inj0
(
Inj1
0
)
)
)
)
(
Inj1
(
Inj1
0
)
)
⟶
x1
(
λ x8 :
ι → ι
.
0
)
(
λ x8 :
ι →
ι →
ι → ι
.
Inj1
0
)
(
λ x8 x9 x10 .
x10
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→ ι
.
∀ x5 .
∀ x6 :
(
ι →
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x7 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
x1
(
λ x8 :
ι → ι
.
Inj1
(
setsum
(
x7
(
λ x9 .
λ x10 :
ι → ι
.
0
)
)
(
setsum
0
0
)
)
)
(
λ x8 :
ι →
ι →
ι → ι
.
x6
(
λ x9 x10 .
x9
)
(
λ x9 :
ι → ι
.
λ x10 .
x8
0
(
x8
(
setsum
0
0
)
(
Inj1
0
)
(
Inj0
0
)
)
0
)
(
λ x9 .
Inj1
(
Inj0
0
)
)
)
(
λ x8 x9 x10 .
x9
)
⟶
x0
(
λ x8 .
setsum
0
(
Inj1
(
setsum
0
(
x7
(
λ x9 .
λ x10 :
ι → ι
.
0
)
)
)
)
)
0
(
setsum
(
setsum
(
setsum
(
x6
(
λ x8 x9 .
0
)
(
λ x8 :
ι → ι
.
λ x9 .
0
)
(
λ x8 .
0
)
)
0
)
(
setsum
0
(
setsum
0
0
)
)
)
(
x6
(
λ x8 x9 .
x7
(
λ x10 .
λ x11 :
ι → ι
.
Inj1
0
)
)
(
λ x8 :
ι → ι
.
λ x9 .
x8
(
setsum
0
0
)
)
(
λ x8 .
setsum
0
(
x7
(
λ x9 .
λ x10 :
ι → ι
.
0
)
)
)
)
)
)
⟶
(
∀ x4 :
(
ι →
ι →
ι → ι
)
→ ι
.
∀ x5 :
ι →
ι → ι
.
∀ x6 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
∀ x7 .
x0
(
λ x8 .
0
)
(
setsum
(
Inj1
(
x6
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
0
)
(
Inj0
0
)
0
)
)
x7
)
(
setsum
(
x4
(
λ x8 x9 x10 .
Inj0
(
setsum
0
0
)
)
)
0
)
⟶
x0
(
λ x8 .
setsum
(
setsum
(
Inj1
(
Inj0
0
)
)
(
setsum
(
Inj0
0
)
0
)
)
(
x5
0
(
Inj0
(
setsum
0
0
)
)
)
)
(
Inj1
(
Inj1
(
x5
(
x6
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
0
)
0
0
)
(
Inj0
0
)
)
)
)
(
Inj1
(
Inj1
(
Inj1
0
)
)
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
ι →
(
ι →
ι → ι
)
→ ι
.
∀ x7 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
x0
(
λ x8 .
x5
)
0
(
setsum
0
x5
)
⟶
False
)
⟶
False
)
⟶
∀ x0 : ο .
x0
(proof)
Theorem
84b22..
:
(
∀ x0 :
(
(
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι →
ι →
ι → ι
)
→
(
(
ι →
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→ ι
)
→
ι → ο
.
∀ x1 :
(
(
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→ ι
)
→ ι
)
→
(
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ο
.
∀ x2 :
(
(
ι →
ι →
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→
ι → ο
.
∀ x3 :
(
(
ι → ι
)
→
ι →
(
ι →
ι → ι
)
→ ι
)
→
(
ι →
ι →
ι →
ι → ι
)
→
(
(
ι →
ι → ι
)
→
ι → ι
)
→ ο
.
(
∀ x4 :
ι → ι
.
∀ x5 x6 .
∀ x7 :
ι →
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
In
(
x7
(
setsum
0
0
)
(
λ x8 .
0
)
(
setsum
(
setsum
(
setsum
0
0
)
(
Inj0
0
)
)
)
)
(
x7
(
setsum
(
setsum
(
x4
0
)
(
setsum
0
0
)
)
(
x4
(
Inj0
0
)
)
)
(
λ x8 .
setsum
0
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
(
λ x8 .
0
)
)
⟶
x0
(
λ x8 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x9 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 x11 x12 .
setsum
(
x9
(
λ x13 :
ι → ι
.
x13
(
x13
0
)
)
)
(
setsum
0
(
x9
(
λ x13 :
ι → ι
.
0
)
)
)
)
(
λ x8 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x9 .
λ x10 :
ι → ι
.
x7
0
(
λ x11 .
setsum
(
setsum
(
setsum
0
0
)
(
Inj0
0
)
)
(
Inj1
(
setsum
0
0
)
)
)
(
λ x11 .
setsum
(
x8
(
setsum
0
0
)
(
λ x12 .
0
)
(
x8
0
(
λ x12 .
0
)
0
)
)
(
Inj0
0
)
)
)
(
Inj1
(
Inj0
(
setsum
(
Inj1
0
)
0
)
)
)
⟶
x3
(
λ x8 :
ι → ι
.
λ x9 .
λ x10 :
ι →
ι → ι
.
Inj1
(
setsum
(
setsum
(
setsum
0
0
)
x9
)
0
)
)
(
λ x8 x9 x10 x11 .
x8
)
(
λ x8 :
ι →
ι → ι
.
λ x9 .
0
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
ι → ι
.
∀ x7 :
ι →
(
ι → ι
)
→ ι
.
x3
(
λ x8 :
ι → ι
.
λ x9 .
λ x10 :
ι →
ι → ι
.
Inj1
(
Inj1
(
setsum
(
setsum
0
0
)
(
x10
0
0
)
)
)
)
(
λ x8 x9 x10 x11 .
setsum
x9
(
setsum
(
setsum
x11
(
Inj0
0
)
)
x10
)
)
(
λ x8 :
ι →
ι → ι
.
λ x9 .
x8
0
(
Inj0
0
)
)
⟶
x2
(
λ x8 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
λ x9 .
x7
x9
(
λ x10 .
Inj0
(
Inj1
0
)
)
)
0
)
⟶
(
∀ x4 .
∀ x5 :
(
ι → ι
)
→ ι
.
∀ x6 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
∀ x7 :
ι →
(
ι →
ι → ι
)
→ ι
.
x0
(
λ x8 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x9 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 x11 x12 .
x12
)
(
λ x8 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x9 .
λ x10 :
ι → ι
.
x9
)
(
Inj1
(
Inj0
0
)
)
⟶
x2
(
λ x8 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
λ x9 .
0
)
(
Inj1
0
)
)
⟶
(
∀ x4 x5 x6 x7 .
x2
(
λ x8 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
λ x9 .
x7
)
(
setsum
(
setsum
(
setsum
(
Inj0
0
)
(
Inj0
0
)
)
0
)
0
)
⟶
In
(
Inj0
0
)
x7
)
⟶
(
∀ x4 x5 .
∀ x6 :
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
∀ x7 .
In
(
setsum
0
(
setsum
0
0
)
)
x5
⟶
x2
(
λ x8 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
λ x9 .
setsum
(
Inj1
0
)
(
setsum
0
(
x6
(
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 :
ι → ι
.
x11
0
)
0
(
λ x10 .
x7
)
(
Inj0
0
)
)
)
)
0
⟶
x1
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→ ι
.
x6
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
setsum
(
x9
(
λ x11 .
Inj0
0
)
)
0
)
x5
(
λ x9 .
setsum
x7
0
)
x5
)
(
λ x8 :
ι →
(
ι → ι
)
→
ι → ι
.
Inj1
0
)
)
⟶
(
∀ x4 .
∀ x5 :
(
ι →
ι → ι
)
→
ι → ι
.
∀ x6 :
(
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
∀ x7 :
ι →
(
ι →
ι → ι
)
→ ι
.
x1
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→ ι
.
Inj0
0
)
(
λ x8 :
ι →
(
ι → ι
)
→
ι → ι
.
0
)
⟶
x1
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→ ι
.
0
)
(
λ x8 :
ι →
(
ι → ι
)
→
ι → ι
.
Inj1
(
x6
(
λ x9 x10 .
Inj1
(
setsum
0
0
)
)
(
λ x9 :
ι → ι
.
x8
0
(
λ x10 .
setsum
0
0
)
0
)
(
Inj0
0
)
)
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→ ι
.
∀ x5 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
∀ x6 .
∀ x7 :
(
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
ι →
ι → ι
)
→
ι →
ι → ι
.
x2
(
λ x8 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
λ x9 .
Inj0
0
)
0
⟶
x0
(
λ x8 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x9 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 x11 x12 .
setsum
x10
x11
)
(
λ x8 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x9 .
λ x10 :
ι → ι
.
setsum
(
x8
(
x7
(
λ x11 x12 :
ι → ι
.
λ x13 .
setsum
0
0
)
(
λ x11 x12 .
setsum
0
0
)
(
setsum
0
0
)
(
x8
0
(
λ x11 .
0
)
0
)
)
(
λ x11 .
Inj1
0
)
(
Inj1
(
setsum
0
0
)
)
)
0
)
(
x4
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 x10 .
0
)
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
ι →
(
ι → ι
)
→ ι
.
∀ x7 :
(
ι →
ι → ι
)
→
ι → ι
.
x0
(
λ x8 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x9 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 x11 x12 .
0
)
(
λ x8 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x9 .
λ x10 :
ι → ι
.
setsum
(
Inj1
(
Inj0
x9
)
)
x9
)
(
Inj0
(
Inj1
(
Inj0
x4
)
)
)
⟶
x0
(
λ x8 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x9 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 x11 x12 .
x11
)
(
λ x8 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x9 .
λ x10 :
ι → ι
.
Inj1
(
x8
(
Inj0
0
)
(
λ x11 .
Inj0
(
x10
0
)
)
(
Inj0
(
Inj1
0
)
)
)
)
(
Inj1
(
x7
(
λ x8 x9 .
setsum
(
setsum
0
0
)
x8
)
0
)
)
)
⟶
False
)
⟶
∀ x0 : ο .
x0
(proof)
Theorem
286ff..
:
(
∀ x0 :
(
ι → ι
)
→
ι → ο
.
∀ x1 x2 :
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ο
.
∀ x3 :
(
ι →
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι →
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→ ο
.
(
∀ x4 x5 x6 x7 .
In
(
setsum
(
setsum
(
setsum
(
Inj1
0
)
0
)
(
Inj0
(
Inj0
0
)
)
)
(
setsum
(
setsum
0
0
)
(
Inj0
(
setsum
0
0
)
)
)
)
(
setsum
(
setsum
(
setsum
(
setsum
0
0
)
x4
)
x7
)
0
)
⟶
x1
(
λ x8 :
ι → ι
.
setsum
(
setsum
(
Inj0
x5
)
(
Inj0
0
)
)
0
)
(
Inj0
(
setsum
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
(
Inj0
(
Inj0
0
)
)
)
)
(
setsum
(
Inj0
(
setsum
0
(
Inj1
0
)
)
)
0
)
⟶
x3
(
λ x8 .
λ x9 :
(
ι → ι
)
→ ι
.
x9
(
λ x10 .
x8
)
)
x5
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 .
Inj0
0
)
)
⟶
(
∀ x4 :
ι →
ι → ι
.
∀ x5 .
∀ x6 :
ι →
ι → ι
.
∀ x7 :
ι →
(
ι →
ι → ι
)
→ ι
.
x3
(
λ x8 .
λ x9 :
(
ι → ι
)
→ ι
.
setsum
(
x9
(
λ x10 .
setsum
(
setsum
0
0
)
x8
)
)
0
)
0
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 .
setsum
(
x8
(
λ x10 .
x8
(
λ x11 .
setsum
0
0
)
)
)
0
)
⟶
False
)
⟶
(
∀ x4 .
∀ x5 :
ι →
(
ι → ι
)
→ ι
.
∀ x6 :
ι → ι
.
∀ x7 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→
ι → ι
.
x0
(
λ x8 .
0
)
(
x6
(
Inj0
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
)
⟶
x2
(
λ x8 :
ι → ι
.
setsum
(
setsum
(
x8
0
)
0
)
(
x7
(
λ x9 .
0
)
(
λ x9 x10 .
setsum
(
Inj0
0
)
0
)
(
x6
(
Inj0
0
)
)
)
)
0
(
x7
(
λ x8 .
Inj1
(
x5
0
(
λ x9 .
0
)
)
)
(
λ x8 x9 .
x8
)
0
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x6 x7 .
x2
(
λ x8 :
ι → ι
.
x6
)
(
setsum
(
setsum
x4
x7
)
(
setsum
0
0
)
)
(
Inj0
0
)
⟶
x0
(
λ x8 .
Inj0
(
x5
0
(
λ x9 :
ι → ι
.
λ x10 .
Inj1
(
Inj0
0
)
)
(
λ x9 .
0
)
)
)
(
setsum
x6
(
Inj0
(
Inj0
(
Inj1
0
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 :
(
ι → ι
)
→
ι → ι
.
∀ x7 .
x0
(
λ x8 .
0
)
(
Inj1
x4
)
⟶
x1
(
λ x8 :
ι → ι
.
setsum
0
(
Inj0
(
Inj1
(
Inj1
0
)
)
)
)
x4
(
setsum
0
0
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 .
∀ x6 :
ι →
(
ι → ι
)
→ ι
.
∀ x7 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι →
ι →
ι → ι
.
x1
(
λ x8 :
ι → ι
.
setsum
0
x5
)
(
setsum
(
Inj1
0
)
(
setsum
(
Inj0
(
setsum
0
0
)
)
0
)
)
(
Inj1
(
x7
(
λ x8 :
(
ι → ι
)
→ ι
.
x6
(
Inj0
0
)
(
λ x9 .
Inj1
0
)
)
(
Inj1
(
Inj0
0
)
)
(
Inj0
(
setsum
0
0
)
)
0
)
)
⟶
In
(
Inj0
(
Inj0
(
x7
(
λ x8 :
(
ι → ι
)
→ ι
.
x8
(
λ x9 .
0
)
)
x5
(
Inj1
0
)
(
Inj0
0
)
)
)
)
(
x4
x5
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
ι →
ι → ι
.
∀ x7 .
In
(
setsum
x7
(
setsum
0
0
)
)
(
Inj0
x7
)
⟶
x0
(
λ x8 .
x8
)
(
Inj1
0
)
⟶
x0
(
λ x8 .
x6
0
(
setsum
0
(
Inj0
0
)
)
)
(
setsum
(
setsum
(
Inj1
x5
)
0
)
(
setsum
(
x6
0
x4
)
(
setsum
(
Inj1
0
)
(
x6
0
0
)
)
)
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
(
ι → ι
)
→ ι
.
∀ x7 :
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
x0
(
λ x8 .
x6
(
λ x9 .
Inj1
0
)
)
(
Inj1
(
setsum
0
(
Inj1
(
setsum
0
0
)
)
)
)
⟶
False
)
⟶
False
)
⟶
∀ x0 : ο .
x0
(proof)
Theorem
4d46e..
:
(
∀ x0 :
(
ι →
(
ι →
(
ι → ι
)
→ ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→ ο
.
∀ x1 :
(
(
ι →
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
(
ι →
ι → ι
)
→ ι
)
→
ι → ι
)
→
ι →
ι →
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ο
.
∀ x2 :
(
ι →
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
)
→
ι →
ι →
ι →
(
ι → ι
)
→
ι → ο
.
∀ x3 :
(
ι →
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
(
(
(
ι →
ι → ι
)
→ ι
)
→ ι
)
→
(
ι → ι
)
→ ο
.
(
∀ x4 :
ι →
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x5 x6 .
∀ x7 :
(
ι → ι
)
→
ι →
ι → ι
.
In
(
Inj0
x6
)
(
setsum
0
(
setsum
0
0
)
)
⟶
x2
(
λ x8 .
λ x9 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
Inj1
x6
)
(
setsum
(
Inj0
(
Inj1
(
setsum
0
0
)
)
)
(
Inj0
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
)
(
x7
(
λ x8 .
setsum
0
0
)
0
0
)
(
setsum
(
x7
(
setsum
x6
)
(
Inj1
(
Inj1
0
)
)
0
)
x5
)
(
λ x8 .
0
)
(
x7
(
λ x8 .
Inj0
0
)
(
x4
(
setsum
(
Inj1
0
)
(
Inj0
0
)
)
(
λ x8 .
x6
)
(
λ x8 .
0
)
0
)
(
Inj0
(
setsum
x5
(
Inj1
0
)
)
)
)
⟶
x3
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 :
ι → ι
.
0
)
(
λ x8 :
(
ι →
ι → ι
)
→ ι
.
x6
)
(
λ x8 .
x5
)
)
⟶
(
∀ x4 :
(
(
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
ι →
ι →
ι → ι
.
∀ x5 x6 .
∀ x7 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
x3
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 :
ι → ι
.
x11
0
)
(
λ x8 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x8 .
0
)
⟶
x2
(
λ x8 .
λ x9 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
Inj0
(
x7
0
(
Inj0
0
)
(
λ x10 .
0
)
(
Inj0
(
setsum
0
0
)
)
)
)
x6
(
x4
(
λ x8 x9 :
ι → ι
.
0
)
(
x4
(
λ x8 x9 :
ι → ι
.
0
)
(
Inj0
(
Inj0
0
)
)
0
0
)
(
setsum
(
setsum
0
x6
)
(
setsum
(
Inj0
0
)
(
Inj1
0
)
)
)
x6
)
x6
(
λ x8 .
setsum
(
Inj1
(
setsum
(
x7
0
0
(
λ x9 .
0
)
0
)
(
setsum
0
0
)
)
)
(
setsum
(
setsum
0
(
setsum
0
0
)
)
(
setsum
x8
(
Inj0
0
)
)
)
)
(
Inj1
(
x7
(
setsum
(
setsum
0
0
)
0
)
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
(
λ x8 .
Inj0
(
Inj1
0
)
)
0
)
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→ ι
.
∀ x5 x6 x7 .
In
x7
(
setsum
(
Inj0
(
x4
(
λ x8 .
0
)
)
)
0
)
⟶
x2
(
λ x8 .
λ x9 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
(
x4
(
λ x8 .
x5
)
)
(
Inj1
(
Inj0
(
setsum
(
Inj1
0
)
0
)
)
)
(
Inj0
0
)
(
λ x8 .
Inj1
0
)
(
Inj0
(
Inj0
0
)
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
∀ x5 x6 x7 .
x2
(
λ x8 .
λ x9 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
x6
0
x7
(
λ x8 .
setsum
0
(
Inj0
(
Inj1
(
Inj1
0
)
)
)
)
(
x4
(
λ x8 .
0
)
(
λ x8 :
ι → ι
.
Inj1
x6
)
(
setsum
0
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
)
⟶
x3
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 :
ι → ι
.
0
)
(
λ x8 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x8 .
setsum
x5
0
)
)
⟶
(
∀ x4 :
ι →
ι →
ι →
ι → ι
.
∀ x5 .
∀ x6 :
ι →
ι →
ι → ι
.
∀ x7 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
x3
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 :
ι → ι
.
setsum
(
Inj0
(
Inj1
(
x11
0
)
)
)
(
x9
0
)
)
(
λ x8 :
(
ι →
ι → ι
)
→ ι
.
0
)
Inj0
⟶
x1
(
λ x8 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
ι →
ι → ι
)
→ ι
.
λ x10 .
setsum
(
x7
(
x9
(
λ x11 x12 .
setsum
0
0
)
)
(
λ x11 :
ι → ι
.
x10
)
)
0
)
(
Inj1
0
)
x5
(
λ x8 :
ι → ι
.
λ x9 .
0
)
(
λ x8 .
0
)
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 x7 .
x1
(
λ x8 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
ι →
ι → ι
)
→ ι
.
λ x10 .
setsum
(
x9
(
λ x11 x12 .
0
)
)
(
x8
0
(
λ x11 :
ι → ι
.
Inj0
(
x11
0
)
)
)
)
(
Inj0
(
setsum
(
Inj1
0
)
(
setsum
x4
(
setsum
0
0
)
)
)
)
(
setsum
x7
(
Inj1
(
setsum
(
setsum
0
0
)
0
)
)
)
(
λ x8 :
ι → ι
.
λ x9 .
x7
)
(
λ x8 .
0
)
⟶
x1
(
λ x8 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
ι →
ι → ι
)
→ ι
.
λ x10 .
x10
)
(
Inj0
x7
)
0
(
λ x8 :
ι → ι
.
λ x9 .
0
)
(
λ x8 .
x8
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
ι →
ι → ι
.
∀ x7 .
x0
(
λ x8 .
λ x9 :
ι →
(
ι → ι
)
→ ι
.
Inj0
(
Inj1
(
Inj1
(
setsum
0
0
)
)
)
)
(
λ x8 :
ι → ι
.
0
)
⟶
x0
(
λ x8 .
λ x9 :
ι →
(
ι → ι
)
→ ι
.
setsum
(
Inj1
(
Inj1
(
setsum
0
0
)
)
)
(
setsum
(
x9
0
(
λ x10 .
setsum
0
0
)
)
x7
)
)
(
λ x8 :
ι → ι
.
setsum
0
(
x6
(
x6
0
0
)
x5
)
)
)
⟶
(
∀ x4 :
ι →
ι → ι
.
∀ x5 :
ι → ι
.
∀ x6 .
∀ x7 :
ι → ι
.
In
x6
(
x5
(
setsum
(
x4
0
(
Inj1
0
)
)
(
x4
x6
(
Inj0
0
)
)
)
)
⟶
x0
(
λ x8 .
λ x9 :
ι →
(
ι → ι
)
→ ι
.
setsum
(
x9
0
(
λ x10 .
0
)
)
(
x9
(
Inj1
(
x9
0
(
λ x10 .
0
)
)
)
(
λ x10 .
x8
)
)
)
(
λ x8 :
ι → ι
.
x8
0
)
⟶
x1
(
λ x8 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
ι →
ι → ι
)
→ ι
.
λ x10 .
setsum
(
setsum
(
Inj0
(
Inj1
0
)
)
(
Inj1
(
setsum
0
0
)
)
)
(
x8
(
setsum
(
x9
(
λ x11 x12 .
0
)
)
(
setsum
0
0
)
)
(
λ x11 :
ι → ι
.
x8
(
setsum
0
0
)
(
λ x12 :
ι → ι
.
x10
)
)
)
)
(
x4
(
x4
(
x4
(
setsum
0
0
)
(
Inj1
0
)
)
(
x7
0
)
)
(
setsum
(
setsum
(
x4
0
0
)
(
setsum
0
0
)
)
0
)
)
(
x5
(
x4
(
setsum
0
(
x5
0
)
)
0
)
)
(
λ x8 :
ι → ι
.
λ x9 .
Inj0
(
setsum
(
Inj1
(
Inj0
0
)
)
0
)
)
(
λ x8 .
Inj1
(
setsum
(
x7
(
setsum
0
0
)
)
(
Inj1
x6
)
)
)
)
⟶
False
)
⟶
∀ x0 : ο .
x0
(proof)
Theorem
3003b..
:
(
∀ x0 :
(
ι → ι
)
→
ι →
(
ι → ι
)
→ ο
.
∀ x1 :
(
(
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι →
(
ι → ι
)
→ ι
)
→ ο
.
∀ x2 :
(
(
ι → ι
)
→
ι →
(
ι → ι
)
→ ι
)
→
ι → ο
.
∀ x3 :
(
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
ι → ο
.
(
∀ x4 :
ι → ι
.
∀ x5 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x6 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
.
∀ x7 .
In
(
Inj1
0
)
x7
⟶
x3
(
λ x8 :
ι →
(
ι → ι
)
→ ι
.
λ x9 .
Inj1
0
)
(
Inj0
0
)
)
⟶
(
∀ x4 :
ι →
ι →
ι → ι
.
∀ x5 :
ι →
(
ι →
ι → ι
)
→ ι
.
∀ x6 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
∀ x7 .
In
(
setsum
(
x4
(
setsum
x7
(
x6
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
0
)
0
(
λ x8 .
0
)
0
)
)
(
Inj1
(
Inj1
0
)
)
0
)
(
Inj1
0
)
)
(
Inj0
x7
)
⟶
x3
(
λ x8 :
ι →
(
ι → ι
)
→ ι
.
λ x9 .
Inj1
(
setsum
0
(
Inj1
x7
)
)
)
(
x6
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
setsum
(
setsum
x10
0
)
(
Inj1
(
setsum
0
0
)
)
)
(
Inj0
(
x4
0
0
(
setsum
0
0
)
)
)
(
λ x8 .
Inj0
0
)
(
Inj1
0
)
)
⟶
x3
(
λ x8 :
ι →
(
ι → ι
)
→ ι
.
λ x9 .
setsum
(
Inj0
(
x8
x9
(
λ x10 .
Inj0
0
)
)
)
(
Inj1
x9
)
)
(
setsum
(
setsum
(
x5
(
setsum
0
0
)
(
λ x8 x9 .
setsum
0
0
)
)
(
setsum
(
setsum
0
0
)
(
x6
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
0
)
0
(
λ x8 .
0
)
0
)
)
)
x7
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
(
ι →
ι → ι
)
→ ι
.
∀ x7 :
ι → ι
.
x2
(
λ x8 :
ι → ι
.
λ x9 .
λ x10 :
ι → ι
.
setsum
(
setsum
(
setsum
0
(
setsum
0
0
)
)
(
x10
0
)
)
0
)
0
)
⟶
(
∀ x4 :
ι →
ι → ι
.
∀ x5 .
∀ x6 :
(
ι →
ι →
ι → ι
)
→ ι
.
∀ x7 .
x2
(
λ x8 :
ι → ι
.
λ x9 .
λ x10 :
ι → ι
.
x10
(
setsum
(
setsum
(
setsum
0
0
)
0
)
(
x10
(
Inj0
0
)
)
)
)
(
setsum
0
(
setsum
(
x4
(
Inj0
0
)
x5
)
(
Inj1
0
)
)
)
⟶
x2
(
λ x8 :
ι → ι
.
λ x9 .
λ x10 :
ι → ι
.
x8
(
setsum
x7
(
Inj0
x7
)
)
)
(
Inj0
(
setsum
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
(
Inj0
(
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 .
∀ x6 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
∀ x7 .
x1
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→ ι
.
λ x9 .
0
)
(
λ x8 :
ι → ι
.
λ x9 .
λ x10 :
ι → ι
.
0
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
ι →
ι → ι
.
∀ x7 :
(
ι → ι
)
→
(
ι → ι
)
→
ι →
ι → ι
.
In
x5
(
Inj0
(
Inj0
(
x7
(
λ x8 .
x7
(
λ x9 .
0
)
(
λ x9 .
0
)
0
0
)
(
λ x8 .
0
)
(
Inj0
0
)
(
Inj0
0
)
)
)
)
⟶
x1
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→ ι
.
λ x9 .
x6
(
setsum
(
Inj0
(
x6
0
0
)
)
(
setsum
0
0
)
)
(
Inj0
(
x6
(
Inj0
0
)
0
)
)
)
(
λ x8 :
ι → ι
.
λ x9 .
λ x10 :
ι → ι
.
setsum
0
x9
)
⟶
x3
(
λ x8 :
ι →
(
ι → ι
)
→ ι
.
λ x9 .
x7
(
λ x10 .
x10
)
(
λ x10 .
x8
(
Inj0
(
x8
0
(
λ x11 .
0
)
)
)
(
λ x11 .
setsum
x11
(
setsum
0
0
)
)
)
(
setsum
0
(
setsum
(
x7
(
λ x10 .
0
)
(
λ x10 .
0
)
0
0
)
(
Inj0
0
)
)
)
(
setsum
x9
0
)
)
(
Inj1
(
x7
(
λ x8 .
0
)
(
λ x8 .
setsum
(
setsum
0
0
)
(
Inj0
0
)
)
(
x7
(
λ x8 .
Inj0
0
)
(
λ x8 .
Inj0
0
)
(
Inj1
0
)
(
setsum
0
0
)
)
(
x6
(
x6
0
0
)
0
)
)
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→ ι
.
∀ x5 .
∀ x6 :
ι →
ι → ι
.
∀ x7 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
In
(
Inj0
0
)
(
setsum
(
Inj0
(
setsum
(
Inj1
0
)
(
x6
0
0
)
)
)
0
)
⟶
x0
(
setsum
x5
)
(
Inj0
(
x7
(
setsum
(
Inj0
0
)
(
x6
0
0
)
)
(
λ x8 :
ι → ι
.
λ x9 .
setsum
(
Inj0
0
)
0
)
)
)
(
λ x8 .
x6
x5
(
setsum
(
Inj0
x5
)
(
x6
x8
(
setsum
0
0
)
)
)
)
⟶
x0
(
λ x8 .
0
)
(
x4
(
λ x8 .
x5
)
)
(
λ x8 .
Inj0
(
setsum
x5
(
x6
(
setsum
0
0
)
(
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι →
(
ι → ι
)
→ ι
.
∀ x6 x7 :
ι → ι
.
x0
(
λ x8 .
Inj1
(
Inj0
(
x5
(
λ x9 :
(
ι → ι
)
→ ι
.
Inj0
0
)
(
x6
0
)
(
λ x9 .
setsum
0
0
)
)
)
)
(
setsum
0
(
Inj1
0
)
)
(
λ x8 .
0
)
⟶
x0
(
λ x8 .
x5
(
λ x9 :
(
ι → ι
)
→ ι
.
0
)
x8
(
λ x9 .
0
)
)
(
Inj1
(
Inj1
(
x7
0
)
)
)
(
λ x8 .
setsum
(
setsum
(
Inj0
(
x7
0
)
)
(
Inj0
0
)
)
(
Inj1
(
Inj0
(
x7
0
)
)
)
)
)
⟶
False
)
⟶
∀ x0 : ο .
x0
(proof)
Theorem
72ada..
:
(
∀ x0 :
(
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι →
(
(
ι → ι
)
→ ι
)
→
ι → ο
.
∀ x1 :
(
ι →
(
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι →
ι →
ι → ι
)
→
ι →
(
ι →
(
ι → ι
)
→ ι
)
→ ο
.
∀ x2 :
(
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
)
→
ι →
ι → ο
.
∀ x3 :
(
(
ι →
ι →
(
ι → ι
)
→ ι
)
→
ι →
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
)
→
(
(
ι →
ι →
ι → ι
)
→ ι
)
→
ι → ο
.
(
∀ x4 :
ι → ι
.
∀ x5 :
(
(
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
∀ x6 x7 .
x3
(
λ x8 :
ι →
ι →
(
ι → ι
)
→ ι
.
λ x9 .
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 x12 .
Inj1
(
Inj0
x11
)
)
(
λ x8 :
ι →
ι →
ι → ι
.
setsum
x6
(
Inj1
(
Inj0
(
setsum
0
0
)
)
)
)
(
Inj0
(
setsum
(
setsum
(
x4
0
)
0
)
0
)
)
)
⟶
(
∀ x4 :
ι →
(
ι → ι
)
→ ι
.
∀ x5 .
∀ x6 :
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
∀ x7 .
In
(
setsum
0
x5
)
(
setsum
(
Inj0
0
)
(
Inj1
0
)
)
⟶
x3
(
λ x8 :
ι →
ι →
(
ι → ι
)
→ ι
.
λ x9 .
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 x12 .
setsum
(
Inj0
x11
)
(
Inj0
(
Inj0
(
x10
(
λ x13 .
0
)
0
)
)
)
)
(
λ x8 :
ι →
ι →
ι → ι
.
0
)
0
⟶
x3
(
λ x8 :
ι →
ι →
(
ι → ι
)
→ ι
.
λ x9 .
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 x12 .
setsum
0
(
Inj1
(
setsum
(
Inj1
0
)
0
)
)
)
(
λ x8 :
ι →
ι →
ι → ι
.
x5
)
(
setsum
x7
(
Inj0
(
Inj0
0
)
)
)
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
ι → ι
.
x3
(
λ x8 :
ι →
ι →
(
ι → ι
)
→ ι
.
λ x9 .
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 x12 .
x11
)
(
λ x8 :
ι →
ι →
ι → ι
.
x5
)
(
Inj0
x5
)
⟶
x2
(
λ x8 .
x7
x5
)
(
λ x8 :
ι → ι
.
0
)
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 :
ι → ι
.
setsum
(
x8
(
λ x10 .
Inj1
(
setsum
0
0
)
)
)
(
setsum
(
setsum
(
x8
(
λ x10 .
0
)
)
(
x7
0
)
)
(
Inj0
(
Inj0
0
)
)
)
)
(
Inj1
(
Inj1
(
setsum
x5
(
Inj1
0
)
)
)
)
(
setsum
(
Inj1
(
setsum
(
setsum
0
0
)
x5
)
)
(
setsum
(
Inj1
x6
)
(
Inj1
(
Inj1
0
)
)
)
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x5 x6 x7 .
In
(
Inj0
x5
)
(
Inj1
(
Inj1
(
Inj0
0
)
)
)
⟶
x2
(
λ x8 .
x6
)
(
λ x8 :
ι → ι
.
Inj0
(
Inj0
0
)
)
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 :
ι → ι
.
0
)
(
Inj1
(
setsum
0
(
Inj0
0
)
)
)
x5
⟶
x2
(
λ x8 .
0
)
(
λ x8 :
ι → ι
.
x5
)
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 :
ι → ι
.
Inj1
0
)
(
Inj1
x5
)
x6
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 :
(
ι →
ι →
ι → ι
)
→
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x7 .
In
(
setsum
(
Inj1
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
(
setsum
(
Inj0
(
x5
0
)
)
0
)
)
(
Inj1
(
setsum
(
setsum
(
Inj1
0
)
(
setsum
0
0
)
)
(
Inj0
(
x6
(
λ x8 x9 x10 .
0
)
(
λ x8 .
0
)
(
λ x8 .
0
)
)
)
)
)
⟶
x0
(
λ x8 x9 .
setsum
(
setsum
0
0
)
(
x6
(
λ x10 x11 x12 .
Inj0
(
Inj1
0
)
)
(
λ x10 .
0
)
(
λ x10 .
x8
)
)
)
(
λ x8 :
ι → ι
.
Inj0
(
setsum
(
x6
(
λ x9 x10 x11 .
Inj0
0
)
(
λ x9 .
0
)
(
λ x9 .
Inj0
0
)
)
0
)
)
(
Inj0
(
setsum
(
setsum
(
setsum
0
0
)
0
)
(
Inj0
(
setsum
0
0
)
)
)
)
(
λ x8 :
ι → ι
.
Inj0
(
setsum
0
0
)
)
(
setsum
x7
(
Inj0
(
Inj0
0
)
)
)
⟶
x1
(
λ x8 .
λ x9 :
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x10 x11 x12 .
x11
)
(
Inj1
(
setsum
(
Inj0
0
)
0
)
)
(
λ x8 .
λ x9 :
ι → ι
.
0
)
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 x7 .
In
(
Inj0
0
)
(
Inj1
(
setsum
0
(
Inj0
x6
)
)
)
⟶
x1
(
λ x8 .
λ x9 :
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x10 x11 x12 .
0
)
0
(
λ x8 .
λ x9 :
ι → ι
.
x9
(
setsum
0
(
Inj1
x7
)
)
)
⟶
x1
(
λ x8 .
λ x9 :
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x10 x11 x12 .
setsum
(
setsum
0
(
Inj0
(
Inj0
0
)
)
)
(
Inj1
(
x9
(
λ x13 .
setsum
0
0
)
(
λ x13 .
x13
)
x11
)
)
)
x6
(
λ x8 .
λ x9 :
ι → ι
.
setsum
(
setsum
0
0
)
0
)
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 x7 .
In
(
x5
0
)
(
setsum
(
Inj0
(
setsum
0
(
x5
0
)
)
)
(
setsum
x7
(
setsum
(
setsum
0
0
)
0
)
)
)
⟶
x0
(
λ x8 x9 .
0
)
(
λ x8 :
ι → ι
.
x8
(
setsum
(
x8
(
x5
0
)
)
(
Inj0
0
)
)
)
(
Inj1
x6
)
(
λ x8 :
ι → ι
.
Inj1
(
setsum
(
setsum
(
x8
0
)
x6
)
(
Inj1
(
setsum
0
0
)
)
)
)
0
)
⟶
(
∀ x4 .
∀ x5 :
(
ι → ι
)
→ ι
.
∀ x6 .
∀ x7 :
ι → ι
.
x0
(
λ x8 x9 .
x8
)
(
λ x8 :
ι → ι
.
setsum
0
(
setsum
0
(
x7
(
x5
(
λ x9 .
0
)
)
)
)
)
0
(
λ x8 :
ι → ι
.
Inj1
(
Inj0
0
)
)
(
x7
0
)
⟶
x0
(
λ x8 x9 .
0
)
(
λ x8 :
ι → ι
.
x8
0
)
(
setsum
(
setsum
0
(
Inj1
(
Inj1
0
)
)
)
0
)
(
λ x8 :
ι → ι
.
0
)
(
Inj0
(
Inj1
0
)
)
)
⟶
False
)
⟶
∀ x0 : ο .
x0
(proof)
Theorem
8bcc9..
:
(
∀ x0 :
(
ι →
(
ι → ι
)
→ ι
)
→
(
(
ι →
(
ι → ι
)
→ ι
)
→ ι
)
→ ο
.
∀ x1 :
(
ι →
(
ι → ι
)
→
ι →
ι → ι
)
→
(
(
ι →
(
ι → ι
)
→
ι → ι
)
→
ι →
ι →
ι → ι
)
→
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ο
.
∀ x2 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ο
.
∀ x3 :
(
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→ ι
)
→
ι → ο
.
(
∀ x4 :
ι → ι
.
∀ x5 x6 .
∀ x7 :
ι → ι
.
x0
(
λ x8 .
λ x9 :
ι → ι
.
0
)
(
λ x8 :
ι →
(
ι → ι
)
→ ι
.
setsum
0
x5
)
⟶
x3
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
x8
(
λ x9 :
ι → ι
.
Inj1
0
)
x6
)
(
setsum
(
Inj0
0
)
(
setsum
(
Inj1
(
x4
0
)
)
(
Inj1
(
Inj0
0
)
)
)
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x5 :
ι →
(
ι → ι
)
→
ι → ι
.
∀ x6 :
ι →
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
∀ x7 .
x3
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
x8
(
λ x9 :
ι → ι
.
Inj0
x7
)
0
)
(
Inj1
x7
)
⟶
False
)
⟶
(
∀ x4 .
∀ x5 :
(
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x6 :
(
ι →
ι → ι
)
→ ι
.
∀ x7 .
x2
(
λ x8 :
ι → ι
.
λ x9 .
setsum
(
x8
(
setsum
0
(
setsum
0
0
)
)
)
x7
)
(
λ x8 .
λ x9 :
(
ι → ι
)
→
ι → ι
.
x6
(
λ x10 x11 .
setsum
(
setsum
x11
(
setsum
0
0
)
)
x11
)
)
⟶
x2
(
λ x8 :
ι → ι
.
λ x9 .
0
)
(
λ x8 .
λ x9 :
(
ι → ι
)
→
ι → ι
.
Inj1
(
Inj1
0
)
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→ ι
.
∀ x5 x6 x7 .
x2
(
λ x8 :
ι → ι
.
Inj1
)
(
λ x8 .
λ x9 :
(
ι → ι
)
→
ι → ι
.
0
)
⟶
False
)
⟶
(
∀ x4 :
ι →
ι →
ι →
ι → ι
.
∀ x5 x6 .
∀ x7 :
ι → ι
.
In
(
Inj1
0
)
(
setsum
(
Inj0
(
x4
(
setsum
0
0
)
(
Inj1
0
)
(
Inj1
0
)
(
setsum
0
0
)
)
)
0
)
⟶
x1
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 x11 .
setsum
(
Inj1
(
setsum
0
(
Inj1
0
)
)
)
(
x9
(
Inj1
0
)
)
)
(
λ x8 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x9 x10 x11 .
x11
)
(
λ x8 :
(
ι → ι
)
→ ι
.
0
)
⟶
x1
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 x11 .
0
)
(
λ x8 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x9 x10 x11 .
setsum
(
setsum
0
(
Inj0
0
)
)
(
setsum
(
Inj0
0
)
0
)
)
(
λ x8 :
(
ι → ι
)
→ ι
.
setsum
(
Inj0
(
x7
(
setsum
0
0
)
)
)
0
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 x6 x7 .
x1
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 x11 .
setsum
(
Inj0
(
setsum
(
setsum
0
0
)
(
Inj0
0
)
)
)
(
setsum
(
setsum
(
setsum
0
0
)
0
)
(
Inj1
0
)
)
)
(
λ x8 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x9 x10 x11 .
0
)
(
λ x8 :
(
ι → ι
)
→ ι
.
setsum
0
(
Inj0
x6
)
)
⟶
In
(
Inj1
(
Inj1
0
)
)
x7
)
⟶
(
∀ x4 x5 :
ι →
ι → ι
.
∀ x6 x7 .
x0
(
λ x8 .
λ x9 :
ι → ι
.
0
)
(
λ x8 :
ι →
(
ι → ι
)
→ ι
.
x7
)
⟶
x0
(
λ x8 .
λ x9 :
ι → ι
.
x6
)
(
λ x8 :
ι →
(
ι → ι
)
→ ι
.
0
)
)
⟶
(
∀ x4 :
ι →
ι → ι
.
∀ x5 .
∀ x6 x7 :
ι → ι
.
x0
(
λ x8 .
λ x9 :
ι → ι
.
Inj0
(
setsum
0
(
Inj1
0
)
)
)
(
λ x8 :
ι →
(
ι → ι
)
→ ι
.
0
)
⟶
In
(
setsum
0
0
)
(
Inj0
0
)
)
⟶
False
)
⟶
∀ x0 : ο .
x0
(proof)
Theorem
b9f6e..
:
(
∀ x0 :
(
(
ι →
ι →
(
ι → ι
)
→ ι
)
→ ι
)
→
ι →
ι → ο
.
∀ x1 :
(
ι → ι
)
→
ι → ο
.
∀ x2 :
(
(
(
(
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
)
→
ι →
(
ι →
ι → ι
)
→ ο
.
∀ x3 :
(
ι →
(
ι → ι
)
→ ι
)
→
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ο
.
(
∀ x4 :
ι →
ι →
ι →
ι → ι
.
∀ x5 x6 .
∀ x7 :
ι → ι
.
x3
(
λ x8 .
λ x9 :
ι → ι
.
x9
(
Inj1
(
Inj0
x6
)
)
)
(
λ x8 :
(
ι → ι
)
→ ι
.
setsum
(
Inj1
(
setsum
x6
0
)
)
(
Inj0
0
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
∀ x6 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→ ι
.
∀ x7 .
In
(
setsum
(
Inj0
(
setsum
(
Inj0
0
)
0
)
)
(
Inj1
0
)
)
(
Inj0
x7
)
⟶
x3
(
λ x8 .
λ x9 :
ι → ι
.
x8
)
(
λ x8 :
(
ι → ι
)
→ ι
.
Inj0
(
setsum
(
setsum
(
setsum
0
0
)
0
)
(
setsum
(
setsum
0
0
)
0
)
)
)
⟶
x3
(
λ x8 .
λ x9 :
ι → ι
.
0
)
(
λ x8 :
(
ι → ι
)
→ ι
.
0
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
ι →
ι → ι
.
∀ x7 :
(
ι → ι
)
→
ι → ι
.
x1
(
λ x8 .
x5
)
(
setsum
x5
(
x6
(
Inj1
0
)
(
Inj1
(
Inj0
0
)
)
)
)
⟶
x2
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
x6
(
x8
(
λ x9 :
ι → ι
.
0
)
(
λ x9 :
ι → ι
.
λ x10 .
0
)
)
0
)
(
x6
0
x4
)
(
λ x8 x9 .
Inj1
(
x7
(
λ x10 .
Inj1
x9
)
0
)
)
)
⟶
(
∀ x4 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
∀ x5 x6 x7 .
x2
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
Inj1
0
)
0
(
λ x8 x9 .
setsum
(
Inj0
0
)
x7
)
⟶
In
(
Inj0
(
Inj0
(
setsum
x6
(
Inj0
0
)
)
)
)
(
Inj0
(
setsum
(
Inj0
(
setsum
0
0
)
)
(
setsum
(
x4
0
0
(
λ x8 .
0
)
0
)
x7
)
)
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
(
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
∀ x7 .
In
(
Inj1
x5
)
(
Inj1
(
setsum
(
Inj1
(
x6
(
λ x8 x9 :
ι → ι
.
λ x10 .
0
)
(
λ x8 x9 .
0
)
)
)
(
Inj1
(
setsum
0
0
)
)
)
)
⟶
x1
(
λ x8 .
x6
(
λ x9 x10 :
ι → ι
.
λ x11 .
Inj0
0
)
(
λ x9 x10 .
setsum
(
Inj0
0
)
0
)
)
(
setsum
0
(
setsum
(
setsum
0
(
setsum
0
0
)
)
(
setsum
0
0
)
)
)
⟶
x1
(
λ x8 .
0
)
(
setsum
0
(
Inj0
0
)
)
)
⟶
(
∀ x4 .
∀ x5 :
(
ι → ι
)
→
ι → ι
.
∀ x6 x7 .
x1
(
λ x8 .
0
)
(
Inj1
(
setsum
(
Inj1
(
setsum
0
0
)
)
(
Inj1
0
)
)
)
⟶
False
)
⟶
(
∀ x4 x5 .
∀ x6 :
ι → ι
.
∀ x7 .
In
x5
(
setsum
(
setsum
0
0
)
(
Inj1
(
setsum
(
Inj0
0
)
x4
)
)
)
⟶
x1
(
λ x8 .
x7
)
(
Inj1
0
)
⟶
x0
(
λ x8 :
ι →
ι →
(
ι → ι
)
→ ι
.
setsum
(
setsum
x7
0
)
(
x6
0
)
)
0
(
setsum
(
Inj0
(
setsum
0
(
Inj0
0
)
)
)
0
)
)
⟶
(
∀ x4 :
ι →
ι → ι
.
∀ x5 .
∀ x6 :
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
∀ x7 .
x0
(
λ x8 :
ι →
ι →
(
ι → ι
)
→ ι
.
0
)
(
setsum
0
(
Inj0
(
setsum
x5
(
Inj1
0
)
)
)
)
(
setsum
(
Inj0
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
(
Inj0
(
Inj1
0
)
)
)
⟶
In
(
Inj1
(
Inj1
(
Inj1
0
)
)
)
(
setsum
0
(
setsum
0
(
Inj1
0
)
)
)
)
⟶
False
)
⟶
∀ x0 : ο .
x0
(proof)
Theorem
7af28..
:
(
∀ x0 :
(
(
ι →
ι → ι
)
→ ι
)
→
ι → ο
.
∀ x1 :
(
ι → ι
)
→
(
(
(
ι →
ι → ι
)
→
ι → ι
)
→ ι
)
→ ο
.
∀ x2 :
(
ι →
(
ι →
ι →
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
(
ι → ι
)
→
ι →
ι → ο
.
∀ x3 :
(
ι →
(
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
(
ι → ι
)
→
ι →
ι → ι
)
→ ο
.
(
∀ x4 .
∀ x5 :
(
ι →
ι → ι
)
→ ι
.
∀ x6 x7 .
x3
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 :
(
ι → ι
)
→ ι
.
0
)
(
λ x8 :
(
ι → ι
)
→ ι
.
0
)
(
λ x8 :
ι → ι
.
λ x9 x10 .
Inj1
(
setsum
(
Inj0
x9
)
0
)
)
)
⟶
(
∀ x4 x5 x6 x7 .
x3
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 :
(
ι → ι
)
→ ι
.
setsum
(
Inj1
0
)
(
setsum
(
Inj0
(
setsum
0
0
)
)
x7
)
)
(
λ x8 :
(
ι → ι
)
→ ι
.
x6
)
(
λ x8 :
ι → ι
.
λ x9 x10 .
x10
)
⟶
x3
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 :
(
ι → ι
)
→ ι
.
Inj1
(
x10
(
λ x11 .
setsum
(
setsum
0
0
)
0
)
)
)
(
λ x8 :
(
ι → ι
)
→ ι
.
0
)
(
λ x8 :
ι → ι
.
λ x9 x10 .
setsum
x10
x7
)
)
⟶
(
∀ x4 :
(
ι →
(
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
∀ x5 x6 x7 .
In
(
x4
(
λ x8 .
λ x9 :
ι → ι
.
x6
)
(
λ x8 :
ι → ι
.
λ x9 .
Inj1
(
Inj0
(
setsum
0
0
)
)
)
(
setsum
0
(
setsum
(
setsum
0
0
)
0
)
)
x5
)
(
setsum
0
(
setsum
(
setsum
(
setsum
0
0
)
0
)
x7
)
)
⟶
x0
(
λ x8 :
ι →
ι → ι
.
x7
)
(
Inj1
(
setsum
x5
(
Inj1
x6
)
)
)
⟶
x2
(
λ x8 .
λ x9 :
ι →
ι →
ι → ι
.
Inj1
0
)
(
λ x8 .
x5
)
(
λ x8 .
0
)
x6
0
)
⟶
(
∀ x4 :
(
ι →
ι → ι
)
→ ι
.
∀ x5 :
ι →
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x6 :
ι → ι
.
∀ x7 .
In
(
x6
(
Inj0
(
setsum
(
Inj1
0
)
(
Inj1
0
)
)
)
)
(
setsum
(
x5
(
x5
0
(
λ x8 :
ι → ι
.
setsum
0
0
)
(
λ x8 .
Inj1
0
)
(
setsum
0
0
)
)
(
λ x8 :
ι → ι
.
setsum
(
x6
0
)
0
)
(
λ x8 .
x5
0
(
λ x9 :
ι → ι
.
0
)
(
λ x9 .
x7
)
(
setsum
0
0
)
)
0
)
(
x4
(
λ x8 x9 .
Inj1
(
setsum
0
0
)
)
)
)
⟶
x2
(
λ x8 .
λ x9 :
ι →
ι →
ι → ι
.
x6
(
Inj1
x7
)
)
(
λ x8 .
x8
)
(
λ x8 .
setsum
0
0
)
(
x5
0
(
λ x8 :
ι → ι
.
x5
0
(
λ x9 :
ι → ι
.
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
(
λ x9 .
Inj1
(
x6
0
)
)
0
)
(
λ x8 .
setsum
(
x5
(
setsum
0
0
)
(
λ x9 :
ι → ι
.
Inj0
0
)
(
λ x9 .
Inj0
0
)
(
Inj1
0
)
)
(
Inj1
0
)
)
(
x4
(
λ x8 x9 .
0
)
)
)
(
x6
0
)
⟶
x0
(
λ x8 :
ι →
ι → ι
.
x5
(
Inj1
0
)
(
λ x9 :
ι → ι
.
Inj0
0
)
Inj1
(
Inj1
0
)
)
(
Inj1
(
x6
(
Inj0
x7
)
)
)
)
⟶
(
∀ x4 :
(
(
ι →
ι → ι
)
→
ι → ι
)
→
ι → ι
.
∀ x5 x6 x7 .
In
x5
x5
⟶
x1
(
λ x8 .
Inj1
x5
)
(
λ x8 :
(
ι →
ι → ι
)
→
ι → ι
.
0
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 x6 .
∀ x7 :
(
ι → ι
)
→ ι
.
In
(
Inj0
(
setsum
(
Inj0
(
Inj1
0
)
)
0
)
)
(
Inj0
(
setsum
(
x4
(
Inj1
0
)
)
x6
)
)
⟶
x1
(
λ x8 .
0
)
(
λ x8 :
(
ι →
ι → ι
)
→
ι → ι
.
x5
)
⟶
x3
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 :
(
ι → ι
)
→ ι
.
setsum
(
Inj1
(
setsum
0
0
)
)
(
Inj1
x8
)
)
(
λ x8 :
(
ι → ι
)
→ ι
.
Inj1
(
setsum
(
Inj1
0
)
0
)
)
(
λ x8 :
ι → ι
.
λ x9 x10 .
x10
)
)
⟶
(
∀ x4 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
∀ x5 .
∀ x6 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x7 :
ι → ι
.
In
(
Inj0
0
)
(
setsum
(
x6
(
setsum
(
setsum
0
0
)
(
Inj1
0
)
)
(
λ x8 :
ι → ι
.
x5
)
)
(
x6
0
(
λ x8 :
ι → ι
.
x5
)
)
)
⟶
x0
(
λ x8 :
ι →
ι → ι
.
0
)
(
setsum
0
(
Inj1
(
setsum
(
Inj0
0
)
(
x4
(
λ x8 :
ι →
ι → ι
.
λ x9 :
ι → ι
.
0
)
(
λ x8 :
ι → ι
.
0
)
0
0
)
)
)
)
)
⟶
(
∀ x4 :
ι →
(
ι → ι
)
→ ι
.
∀ x5 :
ι →
(
ι →
ι → ι
)
→ ι
.
∀ x6 :
ι →
ι → ι
.
∀ x7 .
x0
(
λ x8 :
ι →
ι → ι
.
Inj1
(
setsum
(
setsum
(
setsum
0
0
)
0
)
(
setsum
(
Inj0
0
)
0
)
)
)
0
⟶
x3
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 :
(
ι → ι
)
→ ι
.
setsum
0
(
x10
(
λ x11 .
setsum
0
0
)
)
)
(
λ x8 :
(
ι → ι
)
→ ι
.
Inj0
(
Inj1
(
Inj1
(
setsum
0
0
)
)
)
)
(
λ x8 :
ι → ι
.
λ x9 x10 .
setsum
(
x8
0
)
x7
)
)
⟶
False
)
⟶
∀ x0 : ο .
x0
(proof)
Theorem
a248f..
:
(
∀ x0 :
(
ι → ι
)
→
ι → ο
.
∀ x1 :
(
(
(
ι →
ι →
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ο
.
∀ x2 :
(
(
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→ ι
)
→ ι
)
→
(
(
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι →
(
(
ι → ι
)
→ ι
)
→ ο
.
∀ x3 :
(
ι → ι
)
→
ι →
(
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→ ο
.
(
∀ x4 :
ι →
ι → ι
.
∀ x5 :
(
(
ι →
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x6 :
(
ι → ι
)
→ ι
.
∀ x7 .
In
(
setsum
0
(
setsum
(
x6
(
λ x8 .
Inj0
0
)
)
0
)
)
(
setsum
(
x6
(
λ x8 .
Inj0
(
setsum
0
0
)
)
)
(
Inj0
(
setsum
(
setsum
0
0
)
(
x6
(
λ x8 .
0
)
)
)
)
)
⟶
x0
(
λ x8 .
setsum
(
Inj1
(
Inj1
(
setsum
0
0
)
)
)
(
x6
(
λ x9 .
Inj0
x8
)
)
)
(
x4
(
Inj1
(
Inj1
(
Inj0
0
)
)
)
(
setsum
0
(
Inj1
(
x6
(
λ x8 .
0
)
)
)
)
)
⟶
x3
(
λ x8 .
x7
)
(
x5
(
λ x8 :
ι →
ι → ι
.
λ x9 .
setsum
0
(
Inj1
(
x8
0
0
)
)
)
)
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
λ x9 .
setsum
(
Inj1
x7
)
(
x6
(
λ x10 .
x10
)
)
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
.
∀ x5 :
ι →
(
ι → ι
)
→ ι
.
∀ x6 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι → ι
.
∀ x7 .
In
(
x4
(
λ x8 :
(
ι → ι
)
→ ι
.
0
)
)
(
Inj1
(
setsum
(
Inj1
0
)
(
setsum
(
Inj0
0
)
(
setsum
0
0
)
)
)
)
⟶
x3
(
λ x8 .
Inj0
0
)
(
Inj0
(
Inj0
(
x5
0
(
λ x8 .
0
)
)
)
)
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
λ x9 .
0
)
⟶
x0
(
λ x8 .
Inj0
(
Inj0
(
Inj1
x8
)
)
)
(
x6
(
λ x8 :
(
ι → ι
)
→ ι
.
x5
(
setsum
0
0
)
(
setsum
(
Inj0
0
)
)
)
(
setsum
(
x4
(
λ x8 :
(
ι → ι
)
→ ι
.
Inj1
0
)
)
0
)
)
)
⟶
(
∀ x4 :
(
ι →
ι → ι
)
→ ι
.
∀ x5 :
(
(
ι → ι
)
→
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x6 :
(
(
ι → ι
)
→ ι
)
→
ι →
ι →
ι → ι
.
∀ x7 .
x3
(
λ x8 .
Inj1
0
)
0
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
λ x9 .
0
)
⟶
x2
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→ ι
.
0
)
(
λ x8 :
ι →
ι → ι
.
λ x9 :
(
ι → ι
)
→ ι
.
setsum
(
x9
(
λ x10 .
x8
(
setsum
0
0
)
0
)
)
(
setsum
0
0
)
)
(
setsum
(
Inj1
(
Inj0
(
setsum
0
0
)
)
)
(
Inj0
0
)
)
(
λ x8 :
ι → ι
.
x7
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
ι →
ι →
ι → ι
.
∀ x7 .
x2
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→ ι
.
x5
)
(
λ x8 :
ι →
ι → ι
.
λ x9 :
(
ι → ι
)
→ ι
.
0
)
(
Inj1
(
Inj0
0
)
)
(
λ x8 :
ι → ι
.
setsum
(
setsum
(
Inj1
(
x6
0
0
0
)
)
(
setsum
x7
(
x8
0
)
)
)
x5
)
⟶
x3
(
λ x8 .
Inj0
(
Inj1
(
setsum
(
Inj0
0
)
(
setsum
0
0
)
)
)
)
(
x6
0
0
0
)
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
λ x9 .
Inj0
(
Inj1
0
)
)
)
⟶
(
∀ x4 x5 x6 x7 .
x3
(
λ x8 .
setsum
(
setsum
(
setsum
(
Inj1
0
)
0
)
(
Inj1
(
setsum
0
0
)
)
)
0
)
(
setsum
(
setsum
(
setsum
0
(
setsum
0
0
)
)
(
setsum
x5
x4
)
)
(
Inj1
0
)
)
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
λ x9 .
x7
)
⟶
x1
(
λ x8 :
(
ι →
ι →
ι → ι
)
→ ι
.
λ x9 .
Inj1
x7
)
(
λ x8 x9 .
setsum
x6
0
)
(
λ x8 .
0
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 x6 x7 .
x1
(
λ x8 :
(
ι →
ι →
ι → ι
)
→ ι
.
λ x9 .
Inj0
(
Inj0
(
setsum
x7
(
setsum
0
0
)
)
)
)
(
λ x8 x9 .
x7
)
(
λ x8 .
0
)
⟶
x3
(
λ x8 .
0
)
0
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
setsum
(
setsum
0
(
x8
(
λ x9 .
x7
)
0
)
)
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
ι → ι
.
∀ x7 .
x0
(
λ x8 .
x5
)
(
Inj0
0
)
⟶
x0
(
λ x8 .
setsum
x5
(
Inj1
(
Inj1
(
x6
0
)
)
)
)
(
setsum
(
Inj1
(
setsum
0
(
Inj1
0
)
)
)
(
setsum
(
x6
x7
)
(
Inj1
(
Inj0
0
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
(
(
ι → ι
)
→
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x6 :
ι →
ι →
ι →
ι → ι
.
∀ x7 :
ι → ι
.
x0
(
λ x8 .
setsum
(
setsum
(
setsum
x8
(
x6
0
0
0
0
)
)
x8
)
(
setsum
0
0
)
)
(
setsum
(
x5
(
λ x8 :
ι → ι
.
λ x9 x10 .
setsum
x9
(
setsum
0
0
)
)
(
λ x8 .
x8
)
)
(
setsum
(
x6
(
setsum
0
0
)
(
setsum
0
0
)
(
Inj1
0
)
(
x7
0
)
)
(
setsum
0
(
x6
0
0
0
0
)
)
)
)
⟶
False
)
⟶
False
)
⟶
∀ x0 : ο .
x0
(proof)
Theorem
f1e3e..
:
(
∀ x0 :
(
ι → ι
)
→
(
ι → ι
)
→
ι → ο
.
∀ x1 :
(
ι → ι
)
→
(
ι → ι
)
→
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ο
.
∀ x2 :
(
ι → ι
)
→
(
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ο
.
∀ x3 :
(
(
ι →
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
)
→
(
(
ι →
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→ ο
.
(
∀ x4 .
∀ x5 :
(
ι → ι
)
→
ι → ι
.
∀ x6 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
∀ x7 .
x2
(
λ x8 .
x7
)
(
λ x8 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
x8
(
λ x9 :
ι → ι
.
λ x10 .
setsum
(
x8
(
λ x11 :
ι → ι
.
λ x12 .
setsum
0
0
)
(
λ x11 .
x8
(
λ x12 :
ι → ι
.
λ x13 .
0
)
(
λ x12 .
0
)
0
)
0
)
(
setsum
(
setsum
0
0
)
x10
)
)
(
λ x9 .
Inj1
0
)
0
)
⟶
x3
(
λ x8 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
setsum
(
Inj0
(
x6
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
0
)
)
)
(
Inj1
0
)
)
(
λ x8 :
ι →
(
ι → ι
)
→ ι
.
λ x9 x10 .
x8
x7
(
λ x11 .
setsum
(
x8
(
Inj0
0
)
(
λ x12 .
x11
)
)
(
Inj1
x11
)
)
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→
ι →
ι → ι
.
∀ x5 x6 x7 .
In
(
Inj1
x5
)
(
x4
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 :
ι → ι
.
Inj1
(
setsum
(
setsum
0
0
)
0
)
)
(
λ x8 x9 .
x9
)
0
(
setsum
0
x6
)
)
⟶
x3
(
λ x8 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
setsum
x6
x6
)
(
λ x8 :
ι →
(
ι → ι
)
→ ι
.
λ x9 x10 .
setsum
(
setsum
(
Inj1
(
Inj1
0
)
)
0
)
(
Inj0
(
Inj0
x7
)
)
)
⟶
x1
(
λ x8 .
setsum
0
0
)
(
λ x8 .
setsum
(
setsum
(
setsum
(
Inj0
0
)
(
Inj1
0
)
)
x5
)
x7
)
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
0
)
)
⟶
(
∀ x4 x5 x6 x7 .
In
(
setsum
(
Inj1
(
Inj0
(
Inj1
0
)
)
)
x5
)
(
Inj1
0
)
⟶
x2
(
λ x8 .
setsum
(
Inj1
0
)
(
Inj1
(
setsum
0
(
setsum
0
0
)
)
)
)
(
λ x8 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
Inj1
0
)
)
⟶
(
∀ x4 :
ι →
(
ι → ι
)
→ ι
.
∀ x5 x6 x7 .
x2
(
λ x8 .
Inj0
0
)
(
λ x8 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
0
)
⟶
x0
(
λ x8 .
x8
)
(
λ x8 .
0
)
(
setsum
(
Inj1
(
Inj1
x7
)
)
(
setsum
(
Inj0
(
Inj0
0
)
)
(
Inj1
(
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 :
ι →
ι → ι
.
∀ x5 :
(
ι →
ι →
ι → ι
)
→
(
ι →
ι → ι
)
→
ι → ι
.
∀ x6 .
∀ x7 :
ι → ι
.
x1
(
λ x8 .
Inj0
(
Inj0
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
)
(
λ x8 .
x8
)
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
Inj0
(
x9
0
)
)
)
⟶
(
∀ x4 .
∀ x5 x6 :
ι →
ι → ι
.
∀ x7 .
In
x7
(
setsum
x7
(
x5
(
x5
(
x6
0
0
)
(
setsum
0
0
)
)
(
x5
(
x6
0
0
)
0
)
)
)
⟶
x1
(
λ x8 .
x7
)
(
λ x8 .
0
)
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
x8
)
⟶
x3
(
λ x8 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
Inj1
(
Inj1
(
setsum
(
setsum
0
0
)
(
Inj0
0
)
)
)
)
(
λ x8 :
ι →
(
ι → ι
)
→ ι
.
λ x9 x10 .
setsum
x9
x7
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
.
∀ x5 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
ι →
ι → ι
)
→
ι → ι
.
∀ x6 :
ι →
ι → ι
.
∀ x7 :
(
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
x0
(
λ x8 .
Inj0
(
Inj1
0
)
)
(
λ x8 .
Inj0
(
x7
(
λ x9 .
setsum
0
(
Inj0
0
)
)
(
λ x9 :
ι → ι
.
Inj1
0
)
x8
0
)
)
(
Inj0
(
setsum
0
(
x4
(
λ x8 :
(
ι → ι
)
→ ι
.
Inj1
0
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
)
→
ι → ι
.
∀ x6 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
∀ x7 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
In
(
x7
(
λ x8 :
ι →
ι → ι
.
λ x9 :
ι → ι
.
x8
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
(
Inj1
(
x6
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
0
)
)
)
)
0
0
)
(
Inj1
(
x6
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
x6
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
setsum
0
0
)
)
)
)
⟶
x0
(
λ x8 .
0
)
(
λ x8 .
0
)
(
Inj0
0
)
⟶
x2
(
λ x8 .
setsum
0
(
setsum
(
Inj1
0
)
(
setsum
(
Inj0
0
)
(
Inj0
0
)
)
)
)
(
λ x8 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
x5
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
Inj1
(
setsum
(
setsum
0
0
)
0
)
)
(
x5
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
setsum
0
(
x10
0
)
)
(
setsum
(
Inj0
0
)
(
Inj0
0
)
)
)
)
)
⟶
False
)
⟶
∀ x0 : ο .
x0
(proof)
Theorem
550a7..
:
(
∀ x0 :
(
(
ι →
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ο
.
∀ x1 :
(
(
ι → ι
)
→
ι →
ι →
(
ι → ι
)
→
ι → ι
)
→
(
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
)
→
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ο
.
∀ x2 :
(
ι → ι
)
→
(
ι → ι
)
→ ο
.
∀ x3 :
(
ι → ι
)
→
ι → ο
.
(
∀ x4 x5 x6 x7 .
In
(
setsum
(
Inj0
0
)
0
)
(
Inj0
(
Inj1
x5
)
)
⟶
x3
(
λ x8 .
setsum
x8
(
setsum
(
setsum
(
Inj0
0
)
0
)
(
setsum
0
x5
)
)
)
x4
)
⟶
(
∀ x4 :
(
(
ι →
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x5 :
ι → ι
.
∀ x6 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→ ι
.
∀ x7 :
ι → ι
.
x3
(
λ x8 .
setsum
(
Inj0
(
Inj1
(
x6
(
λ x9 :
ι →
ι → ι
.
λ x10 :
ι → ι
.
λ x11 .
0
)
0
(
λ x9 .
0
)
)
)
)
(
Inj1
(
setsum
(
setsum
0
0
)
(
Inj0
0
)
)
)
)
(
x5
0
)
⟶
x1
(
λ x8 :
ι → ι
.
λ x9 x10 .
λ x11 :
ι → ι
.
λ x12 .
Inj0
x9
)
(
λ x8 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
x9
(
λ x11 .
setsum
0
(
Inj1
0
)
)
)
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
λ x9 :
ι → ι
.
Inj1
(
setsum
(
setsum
(
x6
(
λ x10 :
ι →
ι → ι
.
λ x11 :
ι → ι
.
λ x12 .
0
)
0
(
λ x10 .
0
)
)
(
setsum
0
0
)
)
0
)
)
)
⟶
(
∀ x4 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
∀ x5 x6 x7 .
In
(
Inj1
(
setsum
0
(
Inj1
(
x4
0
0
(
λ x8 .
0
)
0
)
)
)
)
(
setsum
(
setsum
(
Inj0
(
Inj1
0
)
)
0
)
x5
)
⟶
x1
(
λ x8 :
ι → ι
.
λ x9 x10 .
λ x11 :
ι → ι
.
λ x12 .
Inj1
0
)
(
λ x8 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
Inj1
(
x10
(
setsum
(
x10
0
)
(
setsum
0
0
)
)
)
)
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
λ x9 :
ι → ι
.
0
)
⟶
x2
(
λ x8 .
Inj1
x7
)
(
setsum
(
Inj1
(
Inj0
(
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→ ι
.
∀ x5 x6 .
∀ x7 :
(
ι →
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
In
(
x7
(
λ x8 x9 .
0
)
(
λ x8 x9 .
Inj1
(
setsum
(
x7
(
λ x10 x11 .
0
)
(
λ x10 x11 .
0
)
)
(
setsum
0
0
)
)
)
)
(
Inj0
0
)
⟶
x2
(
λ x8 .
0
)
(
λ x8 .
0
)
⟶
x0
(
λ x8 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
Inj1
(
Inj1
0
)
)
(
λ x8 .
λ x9 x10 :
ι → ι
.
λ x11 .
setsum
(
Inj1
(
Inj1
(
setsum
0
0
)
)
)
(
x9
0
)
)
(
λ x8 .
0
)
(
Inj1
(
x4
(
λ x8 .
x8
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x6 :
ι → ι
.
∀ x7 .
x2
(
λ x8 .
0
)
(
λ x8 .
0
)
⟶
x1
(
λ x8 :
ι → ι
.
λ x9 x10 .
λ x11 :
ι → ι
.
λ x12 .
0
)
(
λ x8 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
0
)
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
λ x9 :
ι → ι
.
setsum
(
setsum
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
(
Inj0
0
)
)
(
Inj1
0
)
)
)
⟶
(
∀ x4 .
∀ x5 :
(
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
∀ x6 :
ι → ι
.
∀ x7 :
(
(
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
x1
(
λ x8 :
ι → ι
.
λ x9 x10 .
λ x11 :
ι → ι
.
λ x12 .
x11
(
Inj1
(
Inj0
x10
)
)
)
(
λ x8 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
0
)
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
λ x9 :
ι → ι
.
0
)
⟶
x3
(
λ x8 .
0
)
(
Inj0
(
Inj1
(
x5
(
λ x8 x9 .
0
)
(
λ x8 :
ι → ι
.
setsum
0
0
)
(
λ x8 .
0
)
)
)
)
)
⟶
(
∀ x4 :
ι →
ι → ι
.
∀ x5 :
ι →
(
ι → ι
)
→ ι
.
∀ x6 :
(
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→ ι
.
∀ x7 :
ι → ι
.
In
(
Inj0
(
Inj1
0
)
)
(
x5
(
Inj0
(
setsum
0
0
)
)
(
λ x8 .
0
)
)
⟶
x0
(
λ x8 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x8 .
λ x9 x10 :
ι → ι
.
λ x11 .
setsum
(
Inj0
(
x10
(
setsum
0
0
)
)
)
(
Inj0
x11
)
)
(
λ x8 .
x6
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 .
setsum
(
setsum
(
x7
0
)
(
Inj0
0
)
)
0
)
0
(
λ x9 .
setsum
(
setsum
(
Inj1
0
)
(
setsum
0
0
)
)
(
setsum
x9
(
x6
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 .
0
)
0
(
λ x10 .
0
)
)
)
)
)
(
setsum
(
setsum
0
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
(
Inj0
0
)
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
∀ x5 x6 .
∀ x7 :
(
(
ι →
ι → ι
)
→ ι
)
→ ι
.
x0
(
λ x8 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
Inj1
x6
)
(
λ x8 .
λ x9 x10 :
ι → ι
.
λ x11 .
0
)
(
λ x8 .
Inj0
(
setsum
(
Inj1
(
setsum
0
0
)
)
0
)
)
(
Inj0
x5
)
⟶
x2
(
λ x8 .
x6
)
(
λ x8 .
x7
(
λ x9 :
ι →
ι → ι
.
setsum
(
setsum
x6
(
setsum
0
0
)
)
0
)
)
)
⟶
False
)
⟶
∀ x0 : ο .
x0
(proof)
Theorem
433fa..
:
(
∀ x0 :
(
(
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
)
→
ι →
ι →
(
(
ι → ι
)
→ ι
)
→
ι → ο
.
∀ x1 :
(
ι →
ι →
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ο
.
∀ x2 :
(
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→
ι → ο
.
∀ x3 :
(
(
ι →
ι → ι
)
→
ι → ι
)
→
ι →
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ο
.
(
∀ x4 x5 x6 .
∀ x7 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
.
In
(
Inj0
0
)
x6
⟶
x0
(
λ x8 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
setsum
(
setsum
(
setsum
(
x7
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 .
0
)
)
(
x7
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 .
0
)
)
)
(
setsum
0
0
)
)
x5
)
(
setsum
(
Inj1
0
)
(
x7
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
Inj1
(
Inj1
0
)
)
)
)
(
Inj1
0
)
(
λ x8 :
ι → ι
.
x7
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 .
0
)
)
(
Inj0
x5
)
⟶
x3
(
λ x8 :
ι →
ι → ι
.
λ x9 .
x8
(
Inj0
0
)
(
Inj0
0
)
)
x5
(
λ x8 :
(
ι → ι
)
→ ι
.
0
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 :
(
ι → ι
)
→ ι
.
∀ x6 x7 .
x3
(
λ x8 :
ι →
ι → ι
.
λ x9 .
Inj0
x6
)
(
setsum
(
setsum
(
setsum
(
Inj0
0
)
(
setsum
0
0
)
)
0
)
(
setsum
0
(
x5
(
λ x8 .
setsum
0
0
)
)
)
)
(
λ x8 :
(
ι → ι
)
→ ι
.
x8
(
λ x9 .
Inj1
(
setsum
0
(
setsum
0
0
)
)
)
)
⟶
x1
(
λ x8 x9 .
λ x10 :
ι → ι
.
x7
)
(
λ x8 .
setsum
(
Inj0
(
setsum
(
Inj0
0
)
0
)
)
x7
)
)
⟶
(
∀ x4 :
(
ι →
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x5 :
ι → ι
.
∀ x6 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x7 :
ι →
(
ι → ι
)
→ ι
.
x2
(
λ x8 x9 .
Inj1
0
)
(
λ x8 :
ι → ι
.
setsum
0
(
x7
(
Inj1
(
setsum
0
0
)
)
(
λ x9 .
Inj1
(
setsum
0
0
)
)
)
)
(
λ x8 :
ι →
ι → ι
.
λ x9 x10 .
x7
(
Inj0
x9
)
(
λ x11 .
x8
(
setsum
(
Inj0
0
)
(
Inj1
0
)
)
x10
)
)
0
⟶
x2
(
λ x8 x9 .
0
)
(
λ x8 :
ι → ι
.
Inj0
0
)
(
λ x8 :
ι →
ι → ι
.
λ x9 x10 .
Inj1
(
Inj0
(
Inj0
(
Inj1
0
)
)
)
)
(
x7
(
x4
(
λ x8 x9 .
setsum
0
(
Inj0
0
)
)
(
λ x8 :
ι → ι
.
λ x9 .
x6
0
(
λ x10 :
ι → ι
.
x7
0
(
λ x11 .
0
)
)
)
(
λ x8 .
Inj1
0
)
)
(
λ x8 .
Inj1
(
Inj0
(
Inj1
0
)
)
)
)
)
⟶
(
∀ x4 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
∀ x5 :
ι → ι
.
∀ x6 :
ι →
ι →
ι →
ι → ι
.
∀ x7 :
ι →
(
ι →
ι → ι
)
→
ι →
ι → ι
.
x2
(
λ x8 x9 .
setsum
x9
x9
)
(
λ x8 :
ι → ι
.
0
)
(
λ x8 :
ι →
ι → ι
.
λ x9 x10 .
Inj0
(
Inj0
(
setsum
0
(
x7
0
(
λ x11 x12 .
0
)
0
0
)
)
)
)
(
Inj0
(
Inj0
(
Inj1
(
setsum
0
0
)
)
)
)
⟶
x1
(
λ x8 x9 .
λ x10 :
ι → ι
.
Inj1
x8
)
(
λ x8 .
setsum
(
Inj0
(
x5
(
Inj0
0
)
)
)
(
x6
0
x8
x8
(
Inj0
(
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x6 x7 .
x2
(
λ x8 x9 .
setsum
0
(
Inj1
0
)
)
(
λ x8 :
ι → ι
.
x6
)
(
λ x8 :
ι →
ι → ι
.
λ x9 x10 .
x9
)
0
⟶
x1
(
λ x8 x9 .
λ x10 :
ι → ι
.
setsum
(
Inj0
(
setsum
(
x10
0
)
(
setsum
0
0
)
)
)
(
setsum
(
setsum
x7
(
Inj1
0
)
)
0
)
)
(
λ x8 .
0
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→ ι
.
∀ x5 .
∀ x6 :
ι → ι
.
∀ x7 :
ι →
(
ι → ι
)
→ ι
.
In
(
Inj1
0
)
(
setsum
0
(
x4
(
λ x8 .
x8
)
)
)
⟶
x1
(
λ x8 x9 .
λ x10 :
ι → ι
.
x7
(
Inj1
0
)
(
λ x11 .
0
)
)
(
λ x8 .
0
)
⟶
x1
(
λ x8 x9 .
λ x10 :
ι → ι
.
x7
(
setsum
(
setsum
x9
0
)
x9
)
(
λ x11 .
setsum
0
x9
)
)
(
setsum
(
setsum
0
(
Inj1
(
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
(
(
ι → ι
)
→ ι
)
→ ι
.
In
(
Inj0
0
)
(
setsum
0
(
setsum
(
setsum
(
Inj0
0
)
(
x7
(
λ x8 :
ι → ι
.
0
)
)
)
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
)
⟶
x0
(
λ x8 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
x8
(
λ x9 :
ι →
ι → ι
.
λ x10 :
ι → ι
.
λ x11 .
0
)
(
λ x9 :
ι → ι
.
λ x10 .
Inj0
(
Inj1
(
setsum
0
0
)
)
)
)
(
setsum
0
(
Inj1
(
setsum
0
(
Inj0
0
)
)
)
)
(
x7
(
λ x8 :
ι → ι
.
Inj1
(
Inj1
x6
)
)
)
(
λ x8 :
ι → ι
.
Inj0
(
x8
x5
)
)
0
⟶
x0
(
λ x8 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
(
Inj0
(
setsum
x5
x6
)
)
0
(
λ x8 :
ι → ι
.
setsum
(
Inj1
(
setsum
0
0
)
)
(
Inj0
x6
)
)
0
)
⟶
(
∀ x4 :
(
ι →
ι → ι
)
→ ι
.
∀ x5 x6 .
∀ x7 :
ι →
ι → ι
.
In
(
setsum
0
0
)
(
Inj1
(
Inj1
(
Inj0
(
Inj0
0
)
)
)
)
⟶
x0
(
λ x8 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
Inj0
0
)
(
Inj1
(
setsum
0
(
Inj1
(
Inj0
0
)
)
)
)
x5
(
λ x8 :
ι → ι
.
setsum
x6
x5
)
(
setsum
(
setsum
(
setsum
0
0
)
0
)
0
)
⟶
x3
(
λ x8 :
ι →
ι → ι
.
λ x9 .
Inj0
0
)
0
(
λ x8 :
(
ι → ι
)
→ ι
.
setsum
0
(
setsum
(
x7
(
x7
0
0
)
(
setsum
0
0
)
)
(
x7
(
setsum
0
0
)
(
setsum
0
0
)
)
)
)
)
⟶
False
)
⟶
∀ x0 : ο .
x0
(proof)
Theorem
6858c..
:
(
∀ x0 :
(
(
ι →
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι →
ι → ι
)
→
(
(
ι →
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ο
.
∀ x1 :
(
ι → ι
)
→
(
(
ι →
ι →
ι → ι
)
→ ι
)
→ ο
.
∀ x2 :
(
(
ι →
ι → ι
)
→
ι →
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ο
.
∀ x3 :
(
ι →
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
ι →
ι → ο
.
(
∀ x4 x5 x6 .
∀ x7 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
.
x3
(
λ x8 .
λ x9 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x10 .
setsum
(
setsum
(
setsum
(
Inj1
0
)
(
Inj0
0
)
)
(
x9
(
λ x11 x12 .
x10
)
(
λ x11 .
Inj1
0
)
)
)
(
x7
(
λ x11 :
(
ι → ι
)
→ ι
.
x9
(
λ x12 x13 .
Inj0
0
)
(
λ x12 .
0
)
)
)
)
(
setsum
(
setsum
(
Inj1
(
setsum
0
0
)
)
0
)
(
Inj1
(
Inj1
(
setsum
0
0
)
)
)
)
(
setsum
(
setsum
(
Inj0
(
setsum
0
0
)
)
(
Inj1
0
)
)
(
Inj0
(
Inj0
(
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x6 x7 .
x3
(
λ x8 .
λ x9 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x10 .
setsum
0
(
setsum
(
setsum
x8
(
Inj0
0
)
)
(
Inj1
(
setsum
0
0
)
)
)
)
(
Inj1
x7
)
(
x5
x4
(
λ x8 x9 .
x7
)
(
λ x8 .
setsum
x6
0
)
(
x5
(
x5
(
setsum
0
0
)
(
λ x8 x9 .
Inj1
0
)
(
λ x8 .
Inj1
0
)
(
Inj0
0
)
)
(
λ x8 x9 .
Inj1
(
setsum
0
0
)
)
(
λ x8 .
setsum
0
0
)
0
)
)
⟶
x1
(
λ x8 .
Inj1
0
)
(
λ x8 :
ι →
ι →
ι → ι
.
x5
(
Inj0
(
Inj0
0
)
)
(
λ x9 x10 .
setsum
0
0
)
(
λ x9 .
x6
)
(
setsum
(
x8
0
x7
(
Inj0
0
)
)
(
x5
0
(
λ x9 x10 .
Inj1
0
)
(
λ x9 .
Inj1
0
)
(
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
(
ι → ι
)
→ ι
.
∀ x6 :
ι → ι
.
∀ x7 .
x2
(
λ x8 :
ι →
ι → ι
.
λ x9 x10 x11 .
0
)
(
λ x8 .
x7
)
(
x6
(
setsum
(
Inj0
0
)
(
setsum
(
setsum
0
0
)
0
)
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 .
∀ x6 :
ι → ι
.
∀ x7 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
In
(
Inj0
(
Inj1
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
)
(
setsum
0
0
)
⟶
x2
(
λ x8 :
ι →
ι → ι
.
λ x9 x10 x11 .
Inj0
(
setsum
(
Inj0
(
Inj0
0
)
)
0
)
)
(
λ x8 .
x7
(
λ x9 :
(
ι → ι
)
→ ι
.
Inj1
(
setsum
0
0
)
)
(
λ x9 x10 .
Inj1
x9
)
)
(
setsum
x5
0
)
⟶
x1
(
λ x8 .
setsum
0
(
x7
(
λ x9 :
(
ι → ι
)
→ ι
.
x6
(
setsum
0
0
)
)
(
λ x9 x10 .
Inj1
(
setsum
0
0
)
)
)
)
(
λ x8 :
ι →
ι →
ι → ι
.
Inj0
(
Inj0
(
Inj0
(
Inj0
0
)
)
)
)
)
⟶
(
∀ x4 :
(
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
∀ x5 x6 x7 .
In
(
setsum
(
setsum
(
x4
(
λ x8 x9 :
ι → ι
.
λ x10 .
0
)
x5
)
(
setsum
(
Inj0
0
)
x6
)
)
0
)
(
Inj0
(
setsum
(
Inj0
(
Inj1
0
)
)
x5
)
)
⟶
x3
(
λ x8 .
λ x9 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x10 .
0
)
0
x7
⟶
x1
(
λ x8 .
0
)
(
λ x8 :
ι →
ι →
ι → ι
.
0
)
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 .
∀ x7 :
(
ι → ι
)
→
ι →
ι → ι
.
x1
(
λ x8 .
0
)
(
λ x8 :
ι →
ι →
ι → ι
.
x6
)
⟶
x0
(
λ x8 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
x7
(
λ x9 .
Inj0
(
Inj1
0
)
)
(
x8
(
Inj1
(
setsum
0
0
)
)
(
λ x9 :
ι → ι
.
λ x10 .
0
)
(
x8
(
setsum
0
0
)
(
λ x9 :
ι → ι
.
λ x10 .
x9
0
)
0
)
)
(
x7
(
λ x9 .
setsum
(
setsum
0
0
)
(
Inj1
0
)
)
(
Inj0
(
setsum
0
0
)
)
x6
)
)
(
λ x8 x9 .
Inj0
)
(
λ x8 :
ι →
ι → ι
.
Inj0
(
setsum
(
setsum
(
Inj1
0
)
(
setsum
0
0
)
)
(
setsum
(
Inj1
0
)
0
)
)
)
(
λ x8 :
ι → ι
.
x6
)
(
λ x8 .
x6
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
ι → ι
.
∀ x6 :
ι → ι
.
∀ x7 .
In
(
setsum
0
(
setsum
(
setsum
(
Inj0
0
)
(
setsum
0
0
)
)
0
)
)
(
Inj1
(
Inj1
x7
)
)
⟶
x0
(
λ x8 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
0
)
(
λ x8 x9 x10 .
Inj0
(
Inj1
x8
)
)
(
λ x8 :
ι →
ι → ι
.
0
)
(
λ x8 :
ι → ι
.
x6
(
setsum
0
(
Inj1
(
x8
0
)
)
)
)
(
λ x8 .
Inj1
(
Inj1
(
Inj0
(
x5
0
0
)
)
)
)
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
ι →
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
x0
(
λ x8 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
x8
(
x8
(
setsum
(
Inj1
0
)
(
x8
0
(
λ x9 :
ι → ι
.
λ x10 .
0
)
0
)
)
(
λ x9 :
ι → ι
.
λ x10 .
Inj0
(
x8
0
(
λ x11 :
ι → ι
.
λ x12 .
0
)
0
)
)
(
setsum
0
0
)
)
(
λ x9 :
ι → ι
.
λ x10 .
0
)
(
setsum
(
Inj1
x6
)
x6
)
)
(
λ x8 x9 x10 .
Inj1
(
setsum
(
Inj0
(
Inj1
0
)
)
x9
)
)
(
λ x8 :
ι →
ι → ι
.
0
)
(
λ x8 :
ι → ι
.
x8
x6
)
(
λ x8 .
setsum
x8
(
Inj1
(
setsum
x5
(
setsum
0
0
)
)
)
)
⟶
x0
(
λ x8 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
x8
0
(
λ x9 :
ι → ι
.
λ x10 .
Inj0
(
setsum
0
0
)
)
(
setsum
x6
(
Inj1
(
Inj1
0
)
)
)
)
(
λ x8 x9 x10 .
0
)
(
λ x8 :
ι →
ι → ι
.
Inj1
(
setsum
x5
0
)
)
(
λ x8 :
ι → ι
.
0
)
(
λ x8 .
setsum
0
0
)
)
⟶
False
)
⟶
∀ x0 : ο .
x0
(proof)
Theorem
33ee6..
:
(
∀ x0 :
(
ι →
ι → ι
)
→
ι → ο
.
∀ x1 :
(
ι → ι
)
→
ι → ο
.
∀ x2 :
(
ι →
ι → ι
)
→
(
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
)
→
ι → ο
.
∀ x3 :
(
ι →
ι →
ι → ι
)
→
ι → ο
.
(
∀ x4 :
ι →
ι → ι
.
∀ x5 :
ι → ι
.
∀ x6 :
(
ι → ι
)
→
ι →
(
ι → ι
)
→ ι
.
∀ x7 .
x2
(
λ x8 x9 .
setsum
0
(
setsum
(
setsum
x8
(
x6
(
λ x10 .
0
)
0
(
λ x10 .
0
)
)
)
x7
)
)
(
λ x8 :
ι → ι
.
λ x9 :
ι →
ι → ι
.
x6
(
λ x10 .
Inj0
(
setsum
0
0
)
)
(
setsum
(
Inj1
0
)
(
setsum
(
Inj1
0
)
(
x8
0
)
)
)
(
λ x10 .
0
)
)
x7
⟶
x3
(
λ x8 x9 x10 .
x9
)
0
)
⟶
(
∀ x4 x5 .
∀ x6 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x7 .
In
(
Inj0
0
)
(
Inj1
(
setsum
0
(
setsum
0
(
setsum
0
0
)
)
)
)
⟶
x3
(
λ x8 x9 x10 .
Inj1
(
Inj0
0
)
)
(
Inj1
0
)
⟶
x1
(
λ x8 .
0
)
(
Inj1
(
Inj0
(
Inj0
(
Inj0
0
)
)
)
)
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
ι → ι
.
In
(
Inj0
0
)
(
Inj0
(
Inj0
(
Inj1
(
Inj0
0
)
)
)
)
⟶
x2
(
λ x8 x9 .
0
)
(
λ x8 :
ι → ι
.
λ x9 :
ι →
ι → ι
.
setsum
(
Inj1
(
setsum
(
Inj0
0
)
0
)
)
x6
)
0
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 :
(
ι →
ι → ι
)
→
ι → ι
.
∀ x6 .
∀ x7 :
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
In
(
Inj0
(
setsum
0
(
setsum
0
(
Inj0
0
)
)
)
)
x6
⟶
x2
(
λ x8 x9 .
setsum
0
x6
)
(
λ x8 :
ι → ι
.
λ x9 :
ι →
ι → ι
.
Inj0
(
x9
0
0
)
)
(
setsum
(
x5
(
λ x8 x9 .
Inj1
0
)
(
x5
(
λ x8 x9 .
x9
)
(
setsum
0
0
)
)
)
0
)
⟶
x0
(
λ x8 x9 .
setsum
(
setsum
x9
(
setsum
(
setsum
0
0
)
0
)
)
x6
)
(
setsum
(
setsum
(
x7
(
Inj1
0
)
(
λ x8 x9 .
setsum
0
0
)
(
λ x8 .
setsum
0
0
)
0
)
(
setsum
(
Inj0
0
)
(
setsum
0
0
)
)
)
(
setsum
(
Inj1
(
Inj1
0
)
)
(
setsum
(
x4
0
)
(
Inj0
0
)
)
)
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→
ι →
ι →
ι → ι
.
∀ x5 :
ι →
(
ι → ι
)
→ ι
.
∀ x6 x7 .
x1
(
λ x8 .
0
)
(
Inj1
0
)
)
⟶
(
∀ x4 x5 x6 x7 .
x1
(
λ x8 .
0
)
x5
⟶
x1
(
λ x8 .
x6
)
0
)
⟶
(
∀ x4 x5 x6 x7 .
In
(
Inj1
(
Inj0
(
Inj1
0
)
)
)
(
Inj1
(
Inj1
0
)
)
⟶
x0
(
λ x8 x9 .
x7
)
(
setsum
0
0
)
)
⟶
(
∀ x4 .
∀ x5 x6 :
ι → ι
.
∀ x7 .
x0
(
λ x8 x9 .
0
)
(
x5
(
Inj0
(
Inj0
0
)
)
)
⟶
x3
(
λ x8 x9 x10 .
0
)
0
)
⟶
False
)
⟶
∀ x0 : ο .
x0
(proof)
Theorem
cc30f..
:
(
∀ x0 :
(
(
(
(
ι → ι
)
→
ι →
ι → ι
)
→ ι
)
→
(
ι →
ι →
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ο
.
∀ x1 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ο
.
∀ x2 :
(
ι → ι
)
→
ι →
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ο
.
∀ x3 :
(
ι → ι
)
→
(
(
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
)
→
ι → ι
)
→ ο
.
(
∀ x4 :
ι →
ι →
(
ι → ι
)
→ ι
.
∀ x5 .
∀ x6 :
ι → ι
.
∀ x7 .
x0
(
λ x8 :
(
(
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
λ x9 :
ι →
ι →
ι → ι
.
setsum
0
(
x9
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
(
Inj1
0
)
0
)
)
(
λ x8 .
x7
)
⟶
x3
(
λ x8 .
Inj0
(
x6
(
setsum
(
Inj0
0
)
(
x6
0
)
)
)
)
(
λ x8 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
λ x9 .
x7
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→ ι
.
∀ x5 :
ι →
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
∀ x6 .
∀ x7 :
(
ι → ι
)
→
ι → ι
.
x3
(
λ x8 .
setsum
(
Inj0
0
)
(
Inj0
0
)
)
(
λ x8 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
λ x9 .
0
)
⟶
x1
(
λ x8 .
λ x9 :
ι → ι
.
0
)
(
Inj1
0
)
)
⟶
(
∀ x4 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
∀ x5 :
(
ι →
(
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x6 x7 .
In
(
Inj1
0
)
(
setsum
x7
(
Inj0
(
setsum
0
(
x4
(
λ x8 :
ι →
ι → ι
.
λ x9 :
ι → ι
.
0
)
)
)
)
)
⟶
x2
(
λ x8 .
setsum
(
Inj1
0
)
(
Inj0
0
)
)
(
Inj1
(
setsum
0
0
)
)
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
setsum
(
setsum
0
(
Inj1
(
Inj0
0
)
)
)
(
setsum
x6
0
)
)
⟶
x2
(
λ x8 .
0
)
x7
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
0
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
∀ x6 x7 .
In
x7
(
Inj1
(
setsum
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
(
x5
(
setsum
0
0
)
(
setsum
0
0
)
(
λ x8 .
0
)
0
)
)
)
⟶
x2
(
λ x8 .
Inj1
x6
)
(
x5
(
Inj0
(
setsum
x6
0
)
)
x7
(
λ x8 .
x7
)
x4
)
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
Inj1
x7
)
⟶
x0
(
λ x8 :
(
(
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
λ x9 :
ι →
ι →
ι → ι
.
0
)
(
λ x8 .
x8
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
∀ x5 :
(
ι → ι
)
→ ι
.
∀ x6 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→ ι
.
∀ x7 :
ι → ι
.
In
(
setsum
(
setsum
(
x6
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 .
setsum
0
0
)
(
setsum
0
0
)
(
λ x8 .
setsum
0
0
)
)
(
Inj0
(
setsum
0
0
)
)
)
(
setsum
0
(
Inj0
(
Inj1
0
)
)
)
)
(
x6
(
λ x8 :
(
ι → ι
)
→ ι
.
x7
)
0
(
λ x8 .
0
)
)
⟶
x1
(
λ x8 .
λ x9 :
ι → ι
.
x9
0
)
(
Inj1
(
setsum
(
x7
(
Inj0
0
)
)
(
x7
(
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
(
(
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
∀ x6 x7 .
In
(
setsum
x4
x7
)
(
Inj1
(
setsum
(
setsum
(
setsum
0
0
)
0
)
x4
)
)
⟶
x1
(
λ x8 .
λ x9 :
ι → ι
.
0
)
0
⟶
x3
(
λ x8 .
x7
)
(
λ x8 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
λ x9 .
setsum
0
x6
)
)
⟶
(
∀ x4 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x5 .
∀ x6 :
ι →
ι →
ι →
ι → ι
.
∀ x7 .
x0
(
λ x8 :
(
(
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
λ x9 :
ι →
ι →
ι → ι
.
0
)
(
λ x8 .
0
)
⟶
x0
(
λ x8 :
(
(
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
λ x9 :
ι →
ι →
ι → ι
.
Inj0
(
setsum
x7
x7
)
)
(
λ x8 .
Inj1
(
Inj1
0
)
)
)
⟶
(
∀ x4 x5 x6 :
ι → ι
.
∀ x7 .
x0
(
λ x8 :
(
(
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
λ x9 :
ι →
ι →
ι → ι
.
x7
)
(
λ x8 .
Inj1
0
)
⟶
In
x7
(
x4
(
setsum
0
(
x4
(
Inj0
0
)
)
)
)
)
⟶
False
)
⟶
∀ x0 : ο .
x0
(proof)
Theorem
4eeed..
:
(
∀ x0 :
(
ι →
(
(
ι →
ι → ι
)
→ ι
)
→ ι
)
→
(
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→ ι
)
→ ο
.
∀ x1 :
(
ι →
ι → ι
)
→
(
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι → ι
)
→
(
ι → ι
)
→
(
ι → ι
)
→
ι → ο
.
∀ x2 :
(
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
)
→
ι →
(
ι → ι
)
→
(
ι → ι
)
→ ο
.
∀ x3 :
(
(
(
ι →
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→
ι → ο
.
(
∀ x4 x5 .
∀ x6 :
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x7 :
ι → ι
.
In
(
x7
0
)
x4
⟶
x0
(
λ x8 .
λ x9 :
(
ι →
ι → ι
)
→ ι
.
Inj1
(
x6
(
λ x10 .
Inj0
0
)
(
λ x10 .
x10
)
)
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
0
)
⟶
x3
(
λ x8 :
(
ι →
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x9 .
λ x10 :
ι →
ι → ι
.
λ x11 x12 .
Inj1
0
)
0
)
⟶
(
∀ x4 .
∀ x5 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x6 .
∀ x7 :
ι → ι
.
In
(
setsum
0
(
Inj1
x6
)
)
(
Inj1
(
Inj1
(
x5
(
Inj1
0
)
(
λ x8 :
ι → ι
.
λ x9 .
0
)
)
)
)
⟶
x3
(
λ x8 :
(
ι →
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x9 .
λ x10 :
ι →
ι → ι
.
λ x11 x12 .
Inj1
0
)
x4
⟶
x2
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
setsum
(
setsum
(
setsum
(
setsum
0
0
)
0
)
(
setsum
(
setsum
0
0
)
(
Inj0
0
)
)
)
0
)
0
(
λ x8 .
0
)
(
λ x8 .
setsum
(
Inj0
(
Inj1
(
x5
0
(
λ x9 :
ι → ι
.
λ x10 .
0
)
)
)
)
0
)
)
⟶
(
∀ x4 .
∀ x5 x6 :
ι → ι
.
∀ x7 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
.
x0
(
λ x8 .
λ x9 :
(
ι →
ι → ι
)
→ ι
.
setsum
0
0
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
x7
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 .
setsum
(
setsum
(
setsum
0
0
)
(
Inj0
0
)
)
(
setsum
(
Inj1
0
)
(
setsum
0
0
)
)
)
)
⟶
x2
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
x6
0
)
0
(
λ x8 .
0
)
(
λ x8 .
0
)
)
⟶
(
∀ x4 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
∀ x5 :
(
ι → ι
)
→ ι
.
∀ x6 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x7 .
x2
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
x8
(
λ x9 :
ι → ι
.
x7
)
)
0
(
λ x8 .
Inj0
(
x6
(
λ x9 .
setsum
x8
(
Inj0
0
)
)
(
λ x9 :
ι → ι
.
λ x10 .
setsum
x7
(
setsum
0
0
)
)
(
λ x9 .
0
)
0
)
)
(
λ x8 .
setsum
x8
(
Inj0
0
)
)
⟶
False
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 :
ι →
ι → ι
.
∀ x6 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι → ι
)
→
ι →
ι → ι
.
∀ x7 :
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
x2
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
Inj0
(
setsum
(
x8
(
λ x9 :
ι → ι
.
Inj1
0
)
)
0
)
)
0
(
λ x8 .
0
)
(
λ x8 .
Inj1
(
Inj0
(
setsum
0
(
setsum
0
0
)
)
)
)
⟶
x1
(
λ x8 x9 .
setsum
0
0
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 .
Inj1
(
setsum
(
setsum
(
x6
(
λ x10 :
(
ι → ι
)
→ ι
.
0
)
(
λ x10 .
0
)
0
0
)
(
setsum
0
0
)
)
(
setsum
0
(
x8
(
λ x10 :
ι → ι
.
0
)
)
)
)
)
(
λ x8 .
Inj0
(
setsum
(
x6
(
λ x9 :
(
ι → ι
)
→ ι
.
x9
(
λ x10 .
0
)
)
(
λ x9 .
0
)
0
0
)
(
x6
(
λ x9 :
(
ι → ι
)
→ ι
.
setsum
0
0
)
(
λ x9 .
x7
0
(
λ x10 x11 .
0
)
(
λ x10 .
0
)
0
)
(
x5
0
0
)
0
)
)
)
(
λ x8 .
setsum
(
Inj0
(
setsum
0
0
)
)
(
Inj1
0
)
)
(
Inj1
(
x5
(
x7
(
Inj0
0
)
(
λ x8 x9 .
setsum
0
0
)
(
λ x8 .
setsum
0
0
)
(
x5
0
0
)
)
(
Inj1
(
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 :
(
(
ι →
ι → ι
)
→ ι
)
→ ι
.
∀ x5 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x6 :
ι → ι
.
∀ x7 .
x1
(
λ x8 x9 .
0
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 .
Inj0
(
x6
0
)
)
(
λ x8 .
0
)
(
λ x8 .
x7
)
(
x6
0
)
⟶
x2
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
0
)
0
(
λ x8 .
Inj1
(
x5
x8
(
λ x9 :
ι → ι
.
0
)
)
)
(
λ x8 .
setsum
(
Inj0
x8
)
(
x6
0
)
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x5 x6 x7 .
In
(
Inj0
x7
)
(
Inj0
x5
)
⟶
x2
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
x5
)
x7
(
λ x8 .
Inj0
(
setsum
(
Inj1
(
setsum
0
0
)
)
0
)
)
(
λ x8 .
0
)
⟶
x0
(
λ x8 .
λ x9 :
(
ι →
ι → ι
)
→ ι
.
x9
(
λ x10 x11 .
x9
(
λ x12 x13 .
x10
)
)
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
Inj0
0
)
)
⟶
(
∀ x4 .
∀ x5 :
(
ι → ι
)
→ ι
.
∀ x6 .
∀ x7 :
(
(
ι → ι
)
→ ι
)
→ ι
.
In
(
Inj1
0
)
(
Inj1
(
setsum
0
0
)
)
⟶
x0
(
λ x8 .
λ x9 :
(
ι →
ι → ι
)
→ ι
.
Inj0
(
setsum
0
(
setsum
(
Inj0
0
)
(
x9
(
λ x10 x11 .
0
)
)
)
)
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
Inj1
0
)
⟶
x0
(
λ x8 .
λ x9 :
(
ι →
ι → ι
)
→ ι
.
Inj1
0
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
setsum
0
(
x5
(
λ x9 .
0
)
)
)
)
⟶
False
)
⟶
∀ x0 : ο .
x0
(proof)
Theorem
66506..
:
(
∀ x0 :
(
(
ι →
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→
ι → ο
.
∀ x1 :
(
ι → ι
)
→
(
ι →
(
ι →
ι → ι
)
→ ι
)
→
(
(
ι →
ι → ι
)
→ ι
)
→
ι → ο
.
∀ x2 :
(
ι → ι
)
→
(
(
(
ι →
ι → ι
)
→ ι
)
→ ι
)
→
ι → ο
.
∀ x3 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι →
ι → ο
.
(
∀ x4 :
(
ι → ι
)
→ ι
.
∀ x5 :
ι → ι
.
∀ x6 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x7 :
(
ι → ι
)
→ ι
.
In
(
Inj1
0
)
(
Inj1
(
x7
(
λ x8 .
setsum
(
Inj0
0
)
(
Inj1
0
)
)
)
)
⟶
x1
(
λ x8 .
Inj1
0
)
(
λ x8 .
λ x9 :
ι →
ι → ι
.
setsum
(
setsum
(
setsum
(
Inj1
0
)
0
)
0
)
(
setsum
(
setsum
(
setsum
0
0
)
0
)
(
setsum
0
(
x9
0
0
)
)
)
)
(
λ x8 :
ι →
ι → ι
.
0
)
(
Inj0
(
Inj0
(
setsum
0
(
x5
0
)
)
)
)
⟶
x3
(
λ x8 .
λ x9 :
ι → ι
.
x6
(
λ x10 :
ι → ι
.
λ x11 .
x10
(
Inj0
(
x9
0
)
)
)
)
(
x6
(
λ x8 :
ι → ι
.
λ x9 .
x6
(
λ x10 :
ι → ι
.
λ x11 .
setsum
(
setsum
0
0
)
(
Inj1
0
)
)
)
)
(
setsum
(
Inj0
0
)
0
)
)
⟶
(
∀ x4 .
∀ x5 :
(
(
ι →
ι → ι
)
→ ι
)
→ ι
.
∀ x6 :
(
(
ι →
ι → ι
)
→ ι
)
→
ι → ι
.
∀ x7 .
x3
(
λ x8 .
λ x9 :
ι → ι
.
setsum
(
setsum
x8
(
setsum
(
Inj1
0
)
(
setsum
0
0
)
)
)
0
)
(
x5
(
λ x8 :
ι →
ι → ι
.
x6
(
λ x9 :
ι →
ι → ι
.
setsum
0
(
setsum
0
0
)
)
x7
)
)
(
x5
(
λ x8 :
ι →
ι → ι
.
Inj0
0
)
)
⟶
In
(
Inj0
(
setsum
(
setsum
0
0
)
(
Inj0
(
setsum
0
0
)
)
)
)
(
Inj0
0
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x5 x6 x7 .
In
(
setsum
(
setsum
0
(
setsum
(
x4
(
λ x8 .
0
)
(
λ x8 :
ι → ι
.
0
)
)
x6
)
)
(
setsum
(
x4
(
λ x8 .
Inj1
0
)
(
λ x8 :
ι → ι
.
setsum
0
0
)
)
0
)
)
(
Inj1
(
Inj1
(
setsum
(
Inj1
0
)
0
)
)
)
⟶
x3
(
λ x8 .
λ x9 :
ι → ι
.
0
)
(
Inj0
(
setsum
x5
x5
)
)
0
⟶
x2
(
λ x8 .
0
)
(
λ x8 :
(
ι →
ι → ι
)
→ ι
.
Inj0
(
x8
(
λ x9 x10 .
0
)
)
)
x6
)
⟶
(
∀ x4 .
∀ x5 :
(
ι →
ι →
ι → ι
)
→
ι → ι
.
∀ x6 .
∀ x7 :
(
ι → ι
)
→
ι → ι
.
In
(
setsum
(
setsum
(
setsum
(
x7
(
λ x8 .
0
)
0
)
0
)
(
x7
(
λ x8 .
Inj1
0
)
(
setsum
0
0
)
)
)
x6
)
(
Inj0
x6
)
⟶
x2
(
λ x8 .
0
)
(
λ x8 :
(
ι →
ι → ι
)
→ ι
.
x5
(
λ x9 x10 x11 .
setsum
(
Inj1
x10
)
(
Inj0
(
Inj0
0
)
)
)
(
x5
(
λ x9 x10 x11 .
Inj0
0
)
0
)
)
(
Inj1
(
setsum
(
setsum
x6
(
Inj1
0
)
)
(
Inj0
(
Inj0
0
)
)
)
)
⟶
x0
(
λ x8 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
x7
(
λ x9 .
0
)
(
setsum
0
0
)
)
(
setsum
(
Inj0
0
)
x6
)
(
λ x8 .
setsum
(
Inj0
(
Inj0
(
Inj0
0
)
)
)
(
setsum
(
x5
(
λ x9 x10 x11 .
Inj1
0
)
(
setsum
0
0
)
)
(
setsum
0
0
)
)
)
(
Inj0
x6
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 :
ι →
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
∀ x6 .
∀ x7 :
(
(
ι → ι
)
→ ι
)
→ ι
.
x0
(
λ x8 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
setsum
(
setsum
(
x5
(
Inj1
0
)
(
λ x9 :
ι → ι
.
setsum
0
0
)
(
λ x9 .
setsum
0
0
)
)
(
x7
(
λ x9 :
ι → ι
.
setsum
0
0
)
)
)
(
setsum
(
setsum
0
(
setsum
0
0
)
)
(
setsum
(
x5
0
(
λ x9 :
ι → ι
.
0
)
(
λ x9 .
0
)
)
(
x8
0
0
(
λ x9 .
0
)
0
)
)
)
)
x6
(
λ x8 .
Inj1
(
Inj1
(
x5
(
x5
0
(
λ x9 :
ι → ι
.
0
)
(
λ x9 .
0
)
)
(
λ x9 :
ι → ι
.
x8
)
(
λ x9 .
Inj1
0
)
)
)
)
0
⟶
x1
(
λ x8 .
setsum
(
setsum
0
0
)
0
)
(
λ x8 .
λ x9 :
ι →
ι → ι
.
x9
x8
(
x9
(
Inj1
(
setsum
0
0
)
)
(
Inj1
(
x9
0
0
)
)
)
)
(
λ x8 :
ι →
ι → ι
.
x6
)
(
Inj1
0
)
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
x1
(
λ x8 .
x7
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
Inj1
(
x7
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
x10
(
λ x11 .
0
)
0
)
)
)
)
(
λ x8 .
λ x9 :
ι →
ι → ι
.
Inj0
0
)
(
λ x8 :
ι →
ι → ι
.
Inj1
(
setsum
0
x6
)
)
(
setsum
0
(
setsum
(
Inj1
0
)
0
)
)
⟶
In
(
setsum
0
(
setsum
0
(
Inj1
(
setsum
0
0
)
)
)
)
(
Inj0
(
setsum
(
Inj1
(
Inj1
0
)
)
(
Inj0
(
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 x7 .
x1
(
λ x8 .
0
)
(
λ x8 .
λ x9 :
ι →
ι → ι
.
x7
)
(
λ x8 :
ι →
ι → ι
.
x5
(
setsum
x7
(
setsum
(
Inj1
0
)
0
)
)
)
x7
⟶
x0
(
λ x8 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
Inj0
(
setsum
(
setsum
x6
x6
)
x7
)
)
0
(
λ x8 .
x8
)
(
Inj0
x7
)
)
⟶
(
∀ x4 x5 :
ι → ι
.
∀ x6 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x7 .
x0
(
λ x8 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
setsum
(
setsum
(
Inj1
(
x5
0
)
)
0
)
(
x6
(
λ x9 :
ι → ι
.
λ x10 .
Inj0
0
)
)
)
(
Inj1
x7
)
(
λ x8 .
x6
(
λ x9 :
ι → ι
.
λ x10 .
x9
0
)
)
x7
⟶
In
(
x6
(
λ x8 :
ι → ι
.
λ x9 .
setsum
(
Inj0
(
Inj0
0
)
)
(
Inj0
(
x8
0
)
)
)
)
(
Inj1
(
setsum
(
x4
(
setsum
0
0
)
)
(
setsum
(
x6
(
λ x8 :
ι → ι
.
λ x9 .
0
)
)
(
Inj0
0
)
)
)
)
)
⟶
False
)
⟶
∀ x0 : ο .
x0
(proof)
Theorem
98889..
:
(
∀ x0 :
(
(
ι →
(
ι →
ι → ι
)
→ ι
)
→
(
ι →
ι →
ι → ι
)
→
ι → ι
)
→
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ο
.
∀ x1 :
(
(
ι →
(
ι →
ι → ι
)
→ ι
)
→
ι →
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι →
ι → ι
)
→ ο
.
∀ x2 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
(
(
ι → ι
)
→
ι →
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ο
.
∀ x3 :
(
ι → ι
)
→
(
ι →
ι →
ι →
ι → ι
)
→ ο
.
(
∀ x4 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
∀ x5 .
∀ x6 :
ι →
ι →
ι →
ι → ι
.
∀ x7 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
x3
(
λ x8 .
Inj0
(
setsum
(
Inj0
0
)
x5
)
)
(
λ x8 x9 x10 x11 .
x10
)
⟶
x3
(
λ x8 .
Inj1
(
Inj0
(
Inj1
(
Inj1
0
)
)
)
)
(
λ x8 x9 x10 x11 .
x11
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x5 :
ι → ι
.
∀ x6 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x7 :
(
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
In
(
x6
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
Inj0
(
Inj1
(
x9
0
)
)
)
)
(
x4
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 :
ι → ι
.
λ x10 .
0
)
)
⟶
x3
(
λ x8 .
Inj1
(
x6
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 .
0
)
)
)
(
λ x8 x9 x10 x11 .
0
)
⟶
x3
(
λ x8 .
0
)
(
λ x8 x9 x10 x11 .
x11
)
)
⟶
(
∀ x4 .
∀ x5 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
∀ x6 x7 .
x2
(
λ x8 :
ι →
ι → ι
.
λ x9 :
ι → ι
.
λ x10 .
Inj0
x7
)
(
λ x8 :
(
ι → ι
)
→
ι →
ι → ι
.
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 :
ι → ι
.
λ x11 .
setsum
(
Inj0
0
)
0
)
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
ι → ι
.
x2
(
λ x8 :
ι →
ι → ι
.
λ x9 :
ι → ι
.
λ x10 .
x9
(
setsum
0
0
)
)
(
λ x8 :
(
ι → ι
)
→
ι →
ι → ι
.
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 :
ι → ι
.
λ x11 .
x9
(
λ x12 .
x9
(
λ x13 .
0
)
(
x10
(
setsum
0
0
)
)
)
(
setsum
(
Inj0
(
x9
(
λ x12 .
0
)
0
)
)
(
setsum
(
setsum
0
0
)
x11
)
)
)
⟶
x3
(
λ x8 .
x7
0
)
(
λ x8 x9 x10 x11 .
x8
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 .
∀ x6 :
ι → ι
.
∀ x7 .
x0
(
λ x8 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x9 :
ι →
ι →
ι → ι
.
λ x10 .
0
)
(
λ x8 :
(
ι → ι
)
→ ι
.
setsum
(
setsum
x7
x5
)
(
setsum
(
Inj1
x5
)
0
)
)
⟶
x1
(
λ x8 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x9 .
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 .
0
)
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 x10 x11 .
setsum
0
(
Inj1
(
Inj1
(
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
ι →
ι → ι
.
∀ x6 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
∀ x7 :
ι →
ι → ι
.
x1
(
λ x8 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x9 .
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 .
0
)
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 x10 x11 .
setsum
(
setsum
(
Inj0
(
Inj0
0
)
)
(
setsum
(
Inj0
0
)
0
)
)
x10
)
⟶
False
)
⟶
(
∀ x4 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x5 x6 x7 .
x0
(
λ x8 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x9 :
ι →
ι →
ι → ι
.
λ x10 .
x9
(
Inj0
(
Inj0
x10
)
)
(
x9
x10
0
(
setsum
(
Inj0
0
)
(
setsum
0
0
)
)
)
x10
)
(
λ x8 :
(
ι → ι
)
→ ι
.
x6
)
⟶
x0
(
λ x8 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x9 :
ι →
ι →
ι → ι
.
λ x10 .
x9
0
(
setsum
(
setsum
(
Inj1
0
)
(
Inj1
0
)
)
0
)
(
setsum
(
setsum
0
0
)
(
Inj1
(
setsum
0
0
)
)
)
)
(
λ x8 :
(
ι → ι
)
→ ι
.
setsum
(
setsum
x5
(
Inj0
0
)
)
(
Inj1
x7
)
)
)
⟶
(
∀ x4 :
(
(
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
∀ x5 :
(
ι → ι
)
→
ι →
ι → ι
.
∀ x6 .
∀ x7 :
(
(
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
In
(
Inj1
(
x5
(
λ x8 .
0
)
(
setsum
(
setsum
0
0
)
x6
)
(
setsum
(
Inj1
0
)
(
x5
(
λ x8 .
0
)
0
0
)
)
)
)
(
Inj1
(
Inj0
0
)
)
⟶
x0
(
λ x8 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x9 :
ι →
ι →
ι → ι
.
λ x10 .
0
)
(
λ x8 :
(
ι → ι
)
→ ι
.
setsum
(
setsum
0
(
x5
(
λ x9 .
0
)
(
Inj0
0
)
0
)
)
(
x8
(
λ x9 .
x8
(
λ x10 .
0
)
)
)
)
⟶
x1
(
λ x8 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x9 .
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 .
x8
(
setsum
(
Inj1
(
setsum
0
0
)
)
0
)
(
λ x12 x13 .
setsum
(
Inj1
x12
)
(
setsum
0
(
Inj1
0
)
)
)
)
(
λ x8 :
(
ι → ι
)
→ ι
.
λ x9 x10 x11 .
setsum
0
(
setsum
(
Inj1
(
setsum
0
0
)
)
(
setsum
(
setsum
0
0
)
x11
)
)
)
)
⟶
False
)
⟶
∀ x0 : ο .
x0
(proof)
Theorem
2082d..
:
(
∀ x0 :
(
(
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→ ι
)
→
ι →
(
ι →
(
ι → ι
)
→ ι
)
→ ο
.
∀ x1 :
(
ι → ι
)
→
(
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
)
→
(
ι →
ι → ι
)
→
ι → ο
.
∀ x2 :
(
ι → ι
)
→
ι →
(
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ο
.
∀ x3 :
(
(
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
)
→
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→
ι →
ι → ο
.
(
∀ x4 x5 .
∀ x6 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
∀ x7 .
x2
(
λ x8 .
0
)
(
x6
(
λ x8 .
λ x9 :
ι → ι
.
Inj1
(
setsum
(
Inj1
0
)
(
setsum
0
0
)
)
)
)
(
λ x8 x9 :
ι → ι
.
λ x10 .
x7
)
(
λ x8 :
ι → ι
.
λ x9 .
Inj1
(
Inj0
(
setsum
(
setsum
0
0
)
0
)
)
)
⟶
x3
(
λ x8 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x10 .
setsum
x7
0
)
(
setsum
(
setsum
(
Inj0
(
setsum
0
0
)
)
x5
)
(
Inj0
0
)
)
(
setsum
0
x4
)
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
(
(
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→ ι
.
x3
(
λ x8 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x10 .
Inj1
(
x7
(
λ x11 :
ι → ι
.
setsum
(
setsum
0
0
)
(
x11
0
)
)
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
(
λ x11 .
x9
(
λ x12 x13 .
Inj0
0
)
(
λ x12 .
Inj1
0
)
0
)
)
)
(
setsum
0
(
Inj0
(
Inj0
(
setsum
0
0
)
)
)
)
(
Inj1
x6
)
⟶
In
(
setsum
(
Inj1
x6
)
x4
)
(
Inj1
x5
)
)
⟶
(
∀ x4 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x5 .
∀ x6 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
∀ x7 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→
ι →
ι → ι
.
In
(
Inj1
x5
)
(
setsum
0
(
Inj1
(
x7
(
λ x8 .
Inj1
0
)
(
λ x8 x9 .
setsum
0
0
)
0
0
)
)
)
⟶
x0
(
λ x8 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
0
)
(
Inj0
0
)
(
λ x8 .
λ x9 :
ι → ι
.
setsum
0
(
x7
(
λ x10 .
x10
)
(
λ x10 x11 .
x11
)
(
Inj0
(
x6
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
0
)
)
)
(
Inj0
0
)
)
)
⟶
x2
(
λ x8 .
x8
)
0
(
λ x8 x9 :
ι → ι
.
λ x10 .
0
)
(
λ x8 :
ι → ι
.
λ x9 .
x7
Inj1
(
λ x10 x11 .
x11
)
(
x8
(
setsum
(
x6
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
0
)
)
x9
)
)
0
)
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
(
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
In
(
Inj0
0
)
(
setsum
(
Inj1
0
)
(
Inj0
(
setsum
(
Inj1
0
)
x4
)
)
)
⟶
x2
(
λ x8 .
0
)
0
(
λ x8 x9 :
ι → ι
.
λ x10 .
Inj0
(
Inj0
(
Inj0
(
Inj1
0
)
)
)
)
(
λ x8 :
ι → ι
.
λ x9 .
setsum
x6
(
setsum
(
x7
(
λ x10 .
0
)
(
setsum
0
0
)
(
λ x10 .
setsum
0
0
)
(
Inj0
0
)
)
0
)
)
⟶
x3
(
λ x8 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x10 .
setsum
(
setsum
(
x9
(
λ x11 x12 .
0
)
(
λ x11 .
x8
(
λ x12 :
ι →
ι → ι
.
λ x13 :
ι → ι
.
0
)
)
(
Inj1
0
)
)
(
setsum
(
setsum
0
0
)
0
)
)
(
x9
(
λ x11 x12 .
x10
)
(
λ x11 .
Inj1
(
setsum
0
0
)
)
(
Inj1
(
Inj0
0
)
)
)
)
(
setsum
(
x7
(
λ x8 .
Inj1
(
x7
(
λ x9 .
0
)
0
(
λ x9 .
0
)
0
)
)
x5
(
λ x8 .
Inj1
0
)
(
Inj1
(
Inj1
0
)
)
)
x6
)
0
)
⟶
(
∀ x4 .
∀ x5 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x6 :
(
ι → ι
)
→ ι
.
∀ x7 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
In
(
Inj0
(
Inj1
(
setsum
0
(
Inj0
0
)
)
)
)
(
Inj1
(
setsum
(
setsum
(
setsum
0
0
)
0
)
(
x7
(
λ x8 .
x7
(
λ x9 .
0
)
(
λ x9 :
ι → ι
.
λ x10 .
0
)
)
(
λ x8 :
ι → ι
.
λ x9 .
Inj0
0
)
)
)
)
⟶
x3
(
λ x8 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x10 .
setsum
(
setsum
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
0
)
(
x7
(
λ x11 .
x10
)
(
λ x11 :
ι → ι
.
λ x12 .
x9
(
λ x13 x14 .
0
)
(
λ x13 .
setsum
0
0
)
(
setsum
0
0
)
)
)
)
(
Inj1
(
Inj1
(
setsum
(
Inj0
0
)
(
setsum
0
0
)
)
)
)
(
Inj0
x4
)
⟶
x1
(
λ x8 .
Inj1
(
x5
0
(
λ x9 :
ι → ι
.
λ x10 .
x10
)
)
)
(
λ x8 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
Inj0
(
Inj1
(
setsum
(
setsum
0
0
)
(
Inj1
0
)
)
)
)
(
λ x8 x9 .
Inj0
(
x7
(
λ x10 .
setsum
(
setsum
0
0
)
(
Inj0
0
)
)
(
λ x10 :
ι → ι
.
λ x11 .
Inj1
(
x10
0
)
)
)
)
(
x7
(
λ x8 .
0
)
(
λ x8 :
ι → ι
.
λ x9 .
setsum
(
x6
(
λ x10 .
0
)
)
0
)
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→ ι
.
∀ x5 x6 .
∀ x7 :
ι → ι
.
x1
(
λ x8 .
0
)
(
λ x8 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
(
λ x8 x9 .
Inj1
(
setsum
x6
x8
)
)
0
⟶
In
(
Inj1
(
setsum
0
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
)
(
Inj0
(
setsum
(
Inj1
x6
)
(
x4
(
λ x8 .
0
)
)
)
)
)
⟶
(
∀ x4 x5 x6 x7 .
In
x7
(
setsum
(
Inj0
(
setsum
0
(
setsum
0
0
)
)
)
x6
)
⟶
x2
(
λ x8 .
Inj0
(
setsum
(
Inj0
x8
)
(
setsum
(
setsum
0
0
)
0
)
)
)
(
Inj0
(
setsum
x5
0
)
)
(
λ x8 x9 :
ι → ι
.
λ x10 .
Inj0
(
Inj1
(
setsum
(
setsum
0
0
)
x7
)
)
)
(
λ x8 :
ι → ι
.
λ x9 .
Inj1
(
setsum
0
(
setsum
0
(
setsum
0
0
)
)
)
)
⟶
x0
(
λ x8 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
Inj0
x7
)
(
Inj1
x5
)
(
λ x8 .
λ x9 :
ι → ι
.
0
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
∀ x7 .
x0
(
λ x8 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
setsum
(
setsum
(
setsum
0
(
Inj0
0
)
)
0
)
(
Inj1
(
Inj1
(
setsum
0
0
)
)
)
)
(
setsum
(
Inj1
(
setsum
x5
0
)
)
x7
)
(
λ x8 .
λ x9 :
ι → ι
.
setsum
(
Inj1
(
setsum
(
x6
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
0
)
)
x8
)
)
x7
)
⟶
x1
(
setsum
(
Inj1
(
Inj1
x7
)
)
)
(
λ x8 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
(
λ x8 x9 .
setsum
x9
(
setsum
(
Inj1
(
setsum
0
0
)
)
x9
)
)
(
Inj0
(
x6
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
setsum
(
setsum
0
0
)
0
)
)
)
)
⟶
False
)
⟶
∀ x0 : ο .
x0
(proof)
Theorem
54407..
:
(
∀ x0 :
(
ι →
ι →
(
ι →
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
(
ι → ι
)
→
ι → ο
.
∀ x1 :
(
ι →
(
ι →
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ο
.
∀ x2 :
(
ι → ι
)
→
(
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι → ι
)
→ ο
.
∀ x3 :
(
ι → ι
)
→
ι → ο
.
(
∀ x4 :
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x5 x6 .
∀ x7 :
ι → ι
.
x0
(
λ x8 x9 .
λ x10 :
ι →
ι → ι
.
Inj1
0
)
(
λ x8 .
setsum
(
x7
(
setsum
0
x8
)
)
(
Inj0
0
)
)
(
λ x8 .
x8
)
(
x7
(
setsum
0
(
Inj0
0
)
)
)
⟶
x3
(
λ x8 .
setsum
x6
(
Inj1
0
)
)
(
Inj0
(
setsum
(
x7
0
)
(
setsum
(
Inj1
0
)
(
Inj1
0
)
)
)
)
)
⟶
(
∀ x4 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x5 x6 x7 .
In
(
x4
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
0
)
(
λ x8 :
ι → ι
.
λ x9 .
x8
0
)
(
λ x8 .
0
)
0
)
(
Inj1
(
Inj0
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
)
⟶
x3
(
λ x8 .
Inj1
0
)
0
⟶
x0
(
λ x8 x9 .
λ x10 :
ι →
ι → ι
.
Inj1
(
setsum
0
x9
)
)
(
λ x8 .
setsum
(
Inj1
(
Inj0
(
Inj1
0
)
)
)
(
Inj0
(
setsum
0
(
Inj1
0
)
)
)
)
(
λ x8 .
x8
)
(
Inj1
(
x4
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
Inj1
(
Inj1
0
)
)
(
λ x8 :
ι → ι
.
λ x9 .
Inj0
0
)
(
λ x8 .
0
)
x6
)
)
)
⟶
(
∀ x4 :
ι →
ι → ι
.
∀ x5 x6 x7 .
x3
(
λ x8 .
setsum
(
setsum
x6
x6
)
x7
)
(
Inj1
0
)
⟶
x2
(
λ x8 .
setsum
0
0
)
(
λ x8 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
0
)
(
λ x8 .
x6
)
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 .
∀ x7 :
ι → ι
.
x2
(
λ x8 .
setsum
x6
(
setsum
0
(
x5
0
)
)
)
(
λ x8 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
0
)
(
λ x8 .
setsum
0
(
x7
(
setsum
(
Inj1
0
)
(
Inj0
0
)
)
)
)
⟶
In
(
setsum
(
Inj0
(
x5
x4
)
)
0
)
(
Inj1
(
Inj1
(
setsum
0
0
)
)
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→ ι
.
∀ x5 :
(
ι →
ι → ι
)
→ ι
.
∀ x6 :
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
∀ x7 :
(
ι →
ι →
ι → ι
)
→
ι → ι
.
In
(
Inj0
(
Inj1
(
x5
(
λ x8 x9 .
0
)
)
)
)
(
x5
(
λ x8 x9 .
x6
(
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 :
ι → ι
.
setsum
(
x11
0
)
(
Inj0
0
)
)
)
)
⟶
x1
(
λ x8 .
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
λ x12 .
x10
)
(
λ x8 :
ι → ι
.
Inj0
(
x5
(
λ x9 x10 .
x9
)
)
)
⟶
x1
(
λ x8 .
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
λ x12 .
Inj0
x10
)
(
λ x8 :
ι → ι
.
Inj1
(
Inj0
(
x5
(
λ x9 x10 .
x8
0
)
)
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 :
ι →
ι → ι
.
∀ x6 .
∀ x7 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
In
(
x5
(
Inj1
(
setsum
(
setsum
0
0
)
(
x4
0
)
)
)
(
x7
(
λ x8 .
setsum
(
Inj0
0
)
(
x5
0
0
)
)
(
λ x8 x9 .
Inj1
(
setsum
0
0
)
)
)
)
x6
⟶
x1
(
λ x8 .
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
λ x12 .
setsum
(
Inj0
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
(
Inj1
(
x9
x10
(
λ x13 .
0
)
(
setsum
0
0
)
)
)
)
(
λ x8 :
ι → ι
.
Inj0
0
)
⟶
x0
(
λ x8 x9 .
λ x10 :
ι →
ι → ι
.
0
)
(
λ x8 .
x8
)
(
λ x8 .
x5
(
x7
(
λ x9 .
x9
)
(
λ x9 x10 .
x8
)
)
(
setsum
0
(
x7
(
λ x9 .
Inj0
0
)
(
λ x9 x10 .
setsum
0
0
)
)
)
)
0
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x5 :
ι →
ι →
(
ι → ι
)
→ ι
.
∀ x6 .
∀ x7 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
.
In
(
x7
(
λ x8 :
(
ι → ι
)
→ ι
.
0
)
)
(
Inj1
(
Inj1
(
x7
(
λ x8 :
(
ι → ι
)
→ ι
.
setsum
0
0
)
)
)
)
⟶
x1
(
λ x8 .
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
λ x12 .
Inj1
0
)
(
λ x8 :
ι → ι
.
x7
(
λ x9 :
(
ι → ι
)
→ ι
.
setsum
(
Inj1
0
)
0
)
)
⟶
x0
(
λ x8 x9 .
λ x10 :
ι →
ι → ι
.
0
)
(
λ x8 .
0
)
(
λ x8 .
Inj1
(
setsum
(
setsum
(
setsum
0
0
)
(
x5
0
0
(
λ x9 .
0
)
)
)
(
Inj1
(
x7
(
λ x9 :
(
ι → ι
)
→ ι
.
0
)
)
)
)
)
(
setsum
0
(
x7
(
λ x8 :
(
ι → ι
)
→ ι
.
Inj0
(
Inj0
0
)
)
)
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→ ι
.
∀ x5 :
(
(
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→
ι →
ι → ι
.
∀ x6 :
ι → ι
.
∀ x7 .
x0
(
λ x8 x9 .
λ x10 :
ι →
ι → ι
.
setsum
x9
(
Inj0
(
x10
(
setsum
0
0
)
0
)
)
)
(
λ x8 .
x5
(
λ x9 :
ι → ι
.
setsum
(
Inj1
0
)
(
setsum
(
setsum
0
0
)
0
)
)
(
λ x9 x10 .
0
)
(
Inj1
(
setsum
(
setsum
0
0
)
(
x6
0
)
)
)
0
)
(
λ x8 .
0
)
(
Inj0
(
x5
(
λ x8 :
ι → ι
.
0
)
(
λ x8 x9 .
Inj0
0
)
(
setsum
0
(
x4
(
λ x8 .
0
)
)
)
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
)
⟶
x1
(
λ x8 .
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
λ x12 .
setsum
x12
(
Inj1
x12
)
)
(
λ x8 :
ι → ι
.
Inj0
(
setsum
(
Inj0
0
)
0
)
)
)
⟶
False
)
⟶
∀ x0 : ο .
x0
(proof)
Theorem
6a8d7..
:
(
∀ x0 :
(
ι →
ι → ι
)
→
(
(
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ο
.
∀ x1 :
(
(
ι → ι
)
→
ι →
ι → ι
)
→
ι → ο
.
∀ x2 :
(
ι →
(
ι →
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
)
→
ι →
(
(
ι → ι
)
→
ι → ι
)
→
ι → ο
.
∀ x3 :
(
(
(
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
ι → ο
.
(
∀ x4 x5 .
∀ x6 :
(
ι → ι
)
→ ι
.
∀ x7 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
x1
(
λ x8 :
ι → ι
.
λ x9 x10 .
Inj1
(
Inj1
(
Inj1
(
Inj0
0
)
)
)
)
0
⟶
x3
(
λ x8 :
(
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x9 .
Inj0
(
x6
(
λ x10 .
setsum
(
setsum
0
0
)
0
)
)
)
(
Inj0
0
)
)
⟶
(
∀ x4 :
(
ι →
(
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x5 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
∀ x6 x7 .
x3
(
λ x8 :
(
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x9 .
x9
)
(
setsum
0
(
setsum
(
setsum
(
Inj0
0
)
0
)
(
x5
(
λ x8 .
x5
(
λ x9 .
0
)
(
λ x9 x10 .
0
)
)
(
λ x8 x9 .
0
)
)
)
)
⟶
x3
(
λ x8 :
(
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x9 .
x9
)
(
Inj1
0
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
ι → ι
.
∀ x6 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x7 :
ι → ι
.
x2
(
λ x8 .
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x10 x11 .
x8
)
(
setsum
(
Inj1
0
)
(
setsum
(
setsum
(
setsum
0
0
)
0
)
(
Inj1
(
setsum
0
0
)
)
)
)
(
λ x8 :
ι → ι
.
λ x9 .
setsum
(
x8
(
Inj0
(
Inj0
0
)
)
)
(
Inj1
(
Inj1
(
setsum
0
0
)
)
)
)
(
Inj0
(
Inj1
(
setsum
(
setsum
0
0
)
x4
)
)
)
⟶
x2
(
λ x8 .
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x10 x11 .
0
)
(
setsum
(
x7
(
setsum
x4
(
Inj1
0
)
)
)
x4
)
(
λ x8 :
ι → ι
.
λ x9 .
x9
)
(
Inj1
(
setsum
0
(
Inj0
(
x7
0
)
)
)
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x5 :
(
ι → ι
)
→ ι
.
∀ x6 .
∀ x7 :
ι → ι
.
x2
(
λ x8 .
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x10 x11 .
setsum
(
setsum
x8
(
x9
(
Inj1
0
)
(
λ x12 .
x11
)
0
)
)
0
)
(
Inj1
(
setsum
(
x4
(
λ x8 .
0
)
(
λ x8 .
x8
)
)
0
)
)
(
λ x8 :
ι → ι
.
λ x9 .
setsum
(
setsum
(
x7
(
Inj1
0
)
)
(
x7
(
Inj0
0
)
)
)
(
Inj1
(
x8
0
)
)
)
(
x5
(
λ x8 .
Inj1
0
)
)
⟶
x1
(
λ x8 :
ι → ι
.
λ x9 x10 .
0
)
(
Inj0
(
Inj1
(
setsum
0
(
Inj0
0
)
)
)
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
∀ x5 :
(
ι → ι
)
→
ι → ι
.
∀ x6 .
∀ x7 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
x2
(
λ x8 .
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x10 x11 .
0
)
0
(
λ x8 :
ι → ι
.
λ x9 .
0
)
(
setsum
0
0
)
⟶
x1
(
λ x8 :
ι → ι
.
λ x9 x10 .
Inj1
0
)
(
x7
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
λ x9 :
ι → ι
.
λ x10 .
setsum
(
Inj0
0
)
0
)
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
(
ι → ι
)
→
ι →
ι → ι
.
∀ x7 .
In
(
Inj0
x4
)
(
setsum
0
(
x6
(
λ x8 .
setsum
(
Inj0
0
)
(
setsum
0
0
)
)
(
setsum
x4
(
Inj1
0
)
)
0
)
)
⟶
x1
(
λ x8 :
ι → ι
.
λ x9 x10 .
x10
)
0
⟶
x2
(
λ x8 .
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x10 x11 .
setsum
0
x8
)
(
x6
(
λ x8 .
setsum
(
setsum
x8
x8
)
0
)
0
(
setsum
x4
(
Inj0
x5
)
)
)
(
λ x8 :
ι → ι
.
λ x9 .
Inj1
0
)
(
setsum
0
(
Inj1
x7
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 .
∀ x6 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x7 .
In
(
x6
0
(
λ x8 :
ι → ι
.
Inj0
0
)
)
x7
⟶
x0
(
λ x8 x9 .
setsum
x9
x9
)
(
λ x8 :
ι → ι
.
λ x9 :
(
ι → ι
)
→ ι
.
x9
(
λ x10 .
setsum
(
Inj1
(
Inj1
0
)
)
0
)
)
⟶
x0
(
λ x8 x9 .
setsum
x9
(
setsum
(
Inj0
(
setsum
0
0
)
)
(
Inj1
(
x6
0
(
λ x10 :
ι → ι
.
0
)
)
)
)
)
(
λ x8 :
ι → ι
.
λ x9 :
(
ι → ι
)
→ ι
.
0
)
)
⟶
(
∀ x4 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
∀ x5 :
ι → ι
.
∀ x6 x7 .
x0
(
λ x8 x9 .
Inj0
0
)
(
λ x8 :
ι → ι
.
λ x9 :
(
ι → ι
)
→ ι
.
Inj0
0
)
⟶
In
(
Inj1
(
setsum
0
(
x4
(
λ x8 :
ι → ι
.
x6
)
(
λ x8 .
x5
0
)
)
)
)
x7
)
⟶
False
)
⟶
∀ x0 : ο .
x0
(proof)
Theorem
9baf5..
:
(
∀ x0 :
(
ι →
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι →
ι → ο
.
∀ x1 :
(
ι →
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι → ο
.
∀ x2 :
(
ι → ι
)
→
(
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→
ι → ο
.
∀ x3 :
(
ι →
(
ι →
ι → ι
)
→ ι
)
→
ι →
ι → ο
.
(
∀ x4 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x5 x6 x7 .
In
(
Inj0
x6
)
(
setsum
(
setsum
0
0
)
(
setsum
x6
(
Inj0
(
setsum
0
0
)
)
)
)
⟶
x2
(
λ x8 .
Inj0
(
Inj0
0
)
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
ι →
ι → ι
.
λ x10 x11 .
x10
)
(
setsum
(
x4
(
λ x8 :
ι →
ι → ι
.
λ x9 :
ι → ι
.
λ x10 .
Inj0
(
setsum
0
0
)
)
)
0
)
⟶
x3
(
λ x8 .
λ x9 :
ι →
ι → ι
.
Inj0
x8
)
x5
(
setsum
(
setsum
(
setsum
0
(
setsum
0
0
)
)
(
Inj0
0
)
)
0
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
∀ x5 :
ι → ι
.
∀ x6 x7 .
x3
(
λ x8 .
λ x9 :
ι →
ι → ι
.
0
)
x7
(
setsum
(
setsum
(
setsum
(
setsum
0
0
)
0
)
(
setsum
(
setsum
0
0
)
(
Inj0
0
)
)
)
(
setsum
0
(
Inj1
(
setsum
0
0
)
)
)
)
⟶
x3
(
λ x8 .
λ x9 :
ι →
ι → ι
.
x7
)
(
setsum
(
x4
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
x7
)
)
x6
)
(
Inj0
(
Inj1
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x6 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
∀ x7 .
In
(
Inj0
0
)
(
setsum
0
(
x5
(
Inj0
(
setsum
0
0
)
)
(
λ x8 :
ι → ι
.
λ x9 .
Inj0
0
)
)
)
⟶
x0
(
λ x8 x9 .
λ x10 :
(
ι → ι
)
→
ι → ι
.
x8
)
x7
(
x6
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
λ x9 :
ι → ι
.
λ x10 .
Inj1
0
)
(
λ x8 x9 .
0
)
)
⟶
x2
(
λ x8 .
x8
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
ι →
ι → ι
.
λ x10 x11 .
x10
)
(
setsum
(
Inj0
0
)
(
x6
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
λ x9 :
ι → ι
.
λ x10 .
Inj0
0
)
(
λ x8 x9 .
x9
)
)
)
)
⟶
(
∀ x4 :
ι →
ι → ι
.
∀ x5 :
ι → ι
.
∀ x6 .
∀ x7 :
ι → ι
.
In
(
Inj0
(
Inj1
0
)
)
(
setsum
(
setsum
(
Inj0
0
)
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
(
setsum
0
(
setsum
(
Inj0
0
)
(
x4
0
0
)
)
)
)
⟶
x2
(
λ x8 .
0
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
ι →
ι → ι
.
λ x10 x11 .
0
)
(
setsum
(
setsum
0
(
setsum
(
setsum
0
0
)
(
Inj0
0
)
)
)
(
Inj1
x6
)
)
⟶
x1
(
λ x8 .
λ x9 :
(
ι → ι
)
→ ι
.
Inj0
0
)
(
x4
0
(
x5
(
setsum
(
Inj1
0
)
0
)
)
)
)
⟶
(
∀ x4 .
∀ x5 x6 :
ι → ι
.
∀ x7 .
x3
(
λ x8 .
λ x9 :
ι →
ι → ι
.
0
)
0
0
⟶
x1
(
λ x8 .
λ x9 :
(
ι → ι
)
→ ι
.
x9
(
λ x10 .
setsum
(
Inj1
(
Inj0
0
)
)
(
setsum
0
0
)
)
)
0
)
⟶
(
∀ x4 x5 x6 x7 .
In
(
Inj0
x6
)
(
setsum
(
setsum
x4
(
setsum
x5
(
setsum
0
0
)
)
)
(
Inj1
(
setsum
x5
0
)
)
)
⟶
x1
(
λ x8 .
λ x9 :
(
ι → ι
)
→ ι
.
x7
)
0
⟶
x2
(
λ x8 .
0
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
ι →
ι → ι
.
λ x10 x11 .
setsum
0
0
)
x5
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
∀ x5 x6 x7 .
In
(
Inj1
0
)
x5
⟶
x1
(
λ x8 .
λ x9 :
(
ι → ι
)
→ ι
.
0
)
0
⟶
x0
(
λ x8 x9 .
λ x10 :
(
ι → ι
)
→
ι → ι
.
Inj1
0
)
(
Inj1
(
Inj1
(
x4
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
0
)
)
)
)
(
Inj1
(
setsum
(
setsum
(
Inj0
0
)
0
)
(
Inj1
(
Inj0
0
)
)
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 .
∀ x6 :
ι → ι
.
∀ x7 .
x0
(
λ x8 x9 .
λ x10 :
(
ι → ι
)
→
ι → ι
.
0
)
(
x4
0
)
x7
⟶
False
)
⟶
False
)
⟶
∀ x0 : ο .
x0
(proof)
Theorem
7fcf2..
:
(
∀ x0 :
(
(
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι → ο
.
∀ x1 :
(
(
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι →
ι →
ι →
ι → ι
)
→
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ο
.
∀ x2 :
(
ι → ι
)
→
(
ι → ι
)
→
(
ι →
(
ι → ι
)
→ ι
)
→ ο
.
∀ x3 :
(
ι →
(
ι →
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→
ι →
ι →
ι →
(
ι → ι
)
→
ι → ο
.
(
∀ x4 x5 x6 x7 .
x2
(
λ x8 .
setsum
x5
0
)
(
λ x8 .
0
)
(
λ x8 .
λ x9 :
ι → ι
.
setsum
0
x8
)
⟶
x3
(
λ x8 .
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x10 .
x7
)
x5
(
Inj0
0
)
(
Inj1
(
Inj0
(
setsum
(
Inj1
0
)
(
setsum
0
0
)
)
)
)
(
λ x8 .
0
)
x7
)
⟶
(
∀ x4 .
∀ x5 :
(
ι →
ι →
ι → ι
)
→
ι →
ι → ι
.
∀ x6 :
(
ι → ι
)
→ ι
.
∀ x7 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
x3
(
λ x8 .
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x10 .
setsum
x8
(
Inj0
0
)
)
0
(
setsum
0
0
)
0
(
λ x8 .
Inj1
(
Inj0
(
Inj0
(
setsum
0
0
)
)
)
)
(
setsum
(
setsum
(
x5
(
λ x8 x9 x10 .
x10
)
(
setsum
0
0
)
0
)
0
)
(
setsum
(
x5
(
λ x8 x9 x10 .
Inj0
0
)
0
0
)
0
)
)
⟶
In
(
x5
(
λ x8 x9 x10 .
Inj1
(
Inj0
(
setsum
0
0
)
)
)
(
Inj1
(
x7
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
x6
(
λ x9 .
0
)
)
(
setsum
0
0
)
(
x7
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
0
)
0
0
)
)
)
(
x7
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
0
)
(
x5
(
λ x8 x9 x10 .
0
)
0
(
Inj0
0
)
)
(
Inj1
x4
)
)
)
(
Inj1
(
Inj0
(
Inj0
x4
)
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 x6 .
∀ x7 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
x0
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
0
)
(
setsum
(
x7
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
Inj1
0
)
(
λ x8 :
ι → ι
.
setsum
(
x8
0
)
0
)
(
setsum
(
setsum
0
0
)
)
(
setsum
(
x4
0
)
(
Inj1
0
)
)
)
(
Inj1
(
setsum
(
setsum
0
0
)
x5
)
)
)
⟶
x2
(
λ x8 .
Inj1
0
)
(
λ x8 .
0
)
(
λ x8 .
λ x9 :
ι → ι
.
0
)
)
⟶
(
∀ x4 x5 .
∀ x6 x7 :
ι → ι
.
x2
(
λ x8 .
0
)
(
λ x8 .
0
)
(
λ x8 .
λ x9 :
ι → ι
.
x8
)
⟶
x2
(
λ x8 .
Inj0
(
Inj0
(
x6
(
setsum
0
0
)
)
)
)
(
λ x8 .
0
)
(
λ x8 .
λ x9 :
ι → ι
.
0
)
)
⟶
(
∀ x4 :
ι →
(
ι →
ι → ι
)
→
ι →
ι → ι
.
∀ x5 .
∀ x6 x7 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
In
(
Inj0
(
x4
(
Inj1
(
Inj1
0
)
)
(
λ x8 x9 .
x6
0
(
λ x10 :
ι → ι
.
λ x11 .
Inj1
0
)
)
(
setsum
0
(
Inj1
0
)
)
0
)
)
(
x7
(
setsum
(
x7
(
setsum
0
0
)
(
λ x8 :
ι → ι
.
λ x9 .
setsum
0
0
)
)
(
setsum
(
x4
0
(
λ x8 x9 .
0
)
0
0
)
(
Inj0
0
)
)
)
(
λ x8 :
ι → ι
.
λ x9 .
setsum
(
Inj0
(
Inj1
0
)
)
0
)
)
⟶
x0
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
x7
0
(
λ x9 :
ι → ι
.
λ x10 .
Inj0
(
Inj1
0
)
)
)
(
setsum
(
x7
(
setsum
(
setsum
0
0
)
(
x4
0
(
λ x8 x9 .
0
)
0
0
)
)
(
λ x8 :
ι → ι
.
λ x9 .
x6
0
(
λ x10 :
ι → ι
.
λ x11 .
setsum
0
0
)
)
)
x5
)
⟶
x1
(
λ x8 :
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
setsum
(
Inj1
(
Inj1
0
)
)
(
Inj1
(
Inj1
0
)
)
)
(
λ x8 x9 x10 x11 .
0
)
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
setsum
(
setsum
(
Inj0
0
)
0
)
(
Inj1
(
Inj1
x10
)
)
)
)
⟶
(
∀ x4 :
(
ι →
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x5 x6 :
ι →
ι → ι
.
∀ x7 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
x1
(
λ x8 :
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
x6
(
Inj1
(
setsum
(
Inj0
0
)
(
x7
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 .
0
)
(
λ x9 :
ι → ι
.
λ x10 .
0
)
0
0
)
)
)
(
setsum
(
Inj0
(
setsum
0
0
)
)
(
setsum
(
Inj0
0
)
0
)
)
)
(
λ x8 x9 x10 x11 .
x8
)
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
0
)
⟶
x3
(
λ x8 .
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
Inj0
)
(
Inj0
(
x7
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
setsum
(
Inj0
0
)
(
Inj1
0
)
)
(
λ x8 :
ι → ι
.
λ x9 .
Inj1
0
)
0
(
Inj0
0
)
)
)
(
setsum
(
setsum
(
x6
(
Inj0
0
)
(
x4
(
λ x8 x9 .
0
)
(
λ x8 :
ι → ι
.
λ x9 .
0
)
)
)
0
)
(
x6
0
(
Inj1
(
Inj1
0
)
)
)
)
(
Inj0
(
Inj1
(
setsum
(
x6
0
0
)
(
Inj0
0
)
)
)
)
(
λ x8 .
x8
)
(
setsum
(
setsum
0
(
Inj0
(
setsum
0
0
)
)
)
(
x7
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
setsum
0
0
)
(
λ x8 :
ι → ι
.
λ x9 .
Inj0
(
Inj0
0
)
)
(
Inj1
(
x4
(
λ x8 x9 .
0
)
(
λ x8 :
ι → ι
.
λ x9 .
0
)
)
)
(
setsum
(
setsum
0
0
)
(
x4
(
λ x8 x9 .
0
)
(
λ x8 :
ι → ι
.
λ x9 .
0
)
)
)
)
)
)
⟶
(
∀ x4 :
(
(
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
∀ x5 .
∀ x6 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x7 .
In
(
setsum
(
setsum
0
(
Inj0
(
Inj0
0
)
)
)
(
x4
(
λ x8 :
ι → ι
.
λ x9 x10 .
Inj0
(
Inj0
0
)
)
)
)
(
x4
(
λ x8 :
ι → ι
.
λ x9 x10 .
0
)
)
⟶
x3
(
λ x8 .
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x10 .
Inj0
(
setsum
x8
x7
)
)
(
Inj0
x7
)
(
Inj0
(
setsum
x7
0
)
)
(
Inj0
(
setsum
(
Inj1
0
)
(
setsum
x5
x7
)
)
)
(
λ x8 .
x8
)
0
⟶
x0
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
x5
)
(
setsum
(
Inj0
0
)
(
Inj0
0
)
)
)
⟶
(
∀ x4 :
ι →
ι → ι
.
∀ x5 :
(
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
∀ x6 x7 .
In
(
Inj0
(
Inj1
(
x5
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
λ x9 x10 .
Inj1
0
)
)
)
)
(
Inj1
(
x4
(
Inj1
0
)
(
setsum
(
setsum
0
0
)
0
)
)
)
⟶
x0
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
0
)
(
Inj1
x7
)
⟶
x1
(
λ x8 :
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
setsum
x7
0
)
(
λ x8 x9 x10 x11 .
setsum
(
Inj0
x9
)
x9
)
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
Inj0
(
setsum
(
x9
0
)
0
)
)
)
⟶
False
)
⟶
∀ x0 : ο .
x0
(proof)
Theorem
e4e0f..
:
(
∀ x0 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι →
ι → ι
)
→
ι → ο
.
∀ x1 :
(
ι →
(
(
ι →
ι → ι
)
→ ι
)
→ ι
)
→
(
ι →
ι →
ι → ι
)
→ ο
.
∀ x2 :
(
ι →
ι → ι
)
→
ι → ο
.
∀ x3 :
(
(
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
)
→
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
)
→
ι →
ι → ο
.
(
∀ x4 .
∀ x5 :
ι →
(
ι → ι
)
→ ι
.
∀ x6 x7 .
In
x6
(
setsum
x6
(
Inj1
(
Inj1
(
Inj1
0
)
)
)
)
⟶
x3
(
λ x8 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
λ x9 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
setsum
(
Inj0
0
)
0
)
x4
(
Inj0
0
)
)
⟶
(
∀ x4 :
(
ι →
ι → ι
)
→
ι → ι
.
∀ x5 .
∀ x6 :
ι → ι
.
∀ x7 .
In
(
Inj1
(
setsum
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
x7
)
)
(
Inj0
(
setsum
(
x6
x7
)
x7
)
)
⟶
x3
(
λ x8 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
λ x9 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
Inj1
(
setsum
0
0
)
)
0
(
Inj0
(
Inj0
(
setsum
(
setsum
0
0
)
(
Inj0
0
)
)
)
)
⟶
x2
(
λ x8 x9 .
0
)
(
setsum
(
Inj0
0
)
(
setsum
(
x6
0
)
(
x6
(
x4
(
λ x8 x9 .
0
)
0
)
)
)
)
)
⟶
(
∀ x4 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι →
ι → ι
.
∀ x5 :
ι →
(
ι → ι
)
→ ι
.
∀ x6 :
(
ι →
(
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
∀ x7 :
(
ι →
(
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
In
(
x5
0
Inj1
)
(
Inj1
(
x4
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
Inj0
(
Inj1
0
)
)
(
λ x8 .
0
)
(
setsum
0
0
)
0
)
)
⟶
x2
(
λ x8 x9 .
Inj1
(
setsum
(
x6
(
λ x10 .
λ x11 :
ι → ι
.
Inj1
0
)
(
λ x10 x11 .
0
)
)
(
x6
(
λ x10 .
λ x11 :
ι → ι
.
0
)
(
λ x10 x11 .
x9
)
)
)
)
(
setsum
(
setsum
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
(
setsum
(
Inj1
0
)
(
Inj1
0
)
)
)
0
)
)
⟶
(
∀ x4 :
ι →
(
ι → ι
)
→ ι
.
∀ x5 .
∀ x6 :
(
(
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
∀ x7 .
x2
(
λ x8 x9 .
setsum
x9
(
Inj1
(
setsum
(
setsum
0
0
)
0
)
)
)
(
setsum
(
x4
(
setsum
(
Inj1
0
)
(
setsum
0
0
)
)
(
λ x8 .
Inj0
x5
)
)
(
setsum
(
x4
(
Inj1
0
)
(
λ x8 .
Inj0
0
)
)
(
Inj1
0
)
)
)
⟶
x3
(
λ x8 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
λ x9 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
Inj0
(
x8
(
λ x10 .
0
)
(
λ x10 :
ι → ι
.
λ x11 .
0
)
0
(
Inj1
(
Inj1
0
)
)
)
)
(
setsum
(
setsum
(
Inj0
(
setsum
0
0
)
)
x7
)
x5
)
0
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 .
∀ x7 :
(
ι → ι
)
→
ι → ι
.
In
(
Inj0
(
x7
(
λ x8 .
0
)
0
)
)
(
Inj1
(
Inj0
x4
)
)
⟶
x1
(
λ x8 .
λ x9 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x8 x9 x10 .
0
)
)
⟶
(
∀ x4 x5 .
∀ x6 x7 :
ι → ι
.
In
(
setsum
0
(
setsum
(
x7
0
)
x5
)
)
(
Inj1
0
)
⟶
x1
(
λ x8 .
λ x9 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x8 x9 x10 .
Inj1
0
)
⟶
x1
(
λ x8 .
λ x9 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x8 x9 x10 .
Inj1
x8
)
)
⟶
(
∀ x4 :
ι →
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
∀ x5 x6 .
∀ x7 :
(
ι → ι
)
→ ι
.
In
(
x4
(
Inj0
(
Inj1
x5
)
)
(
λ x8 :
ι → ι
.
setsum
(
x7
(
λ x9 .
x8
0
)
)
(
x8
(
setsum
0
0
)
)
)
(
λ x8 .
0
)
)
(
setsum
(
Inj1
x6
)
x6
)
⟶
x2
(
λ x8 .
Inj1
)
(
x7
(
λ x8 .
x7
(
λ x9 .
0
)
)
)
⟶
x0
(
λ x8 .
0
)
(
λ x8 :
ι → ι
.
λ x9 x10 .
setsum
(
setsum
(
Inj0
x9
)
(
Inj1
(
Inj1
0
)
)
)
(
Inj0
(
setsum
(
Inj0
0
)
(
x8
0
)
)
)
)
(
setsum
x5
(
setsum
(
setsum
0
(
Inj1
0
)
)
(
x4
0
(
λ x8 :
ι → ι
.
Inj0
0
)
(
λ x8 .
x6
)
)
)
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
∀ x5 :
(
(
ι →
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x6 x7 .
x0
(
λ x8 .
0
)
(
λ x8 :
ι → ι
.
λ x9 .
setsum
0
)
x6
⟶
x0
(
λ x8 .
x7
)
(
λ x8 :
ι → ι
.
λ x9 x10 .
x7
)
(
setsum
(
Inj0
(
Inj1
(
x4
(
λ x8 :
(
ι → ι
)
→ ι
.
0
)
(
λ x8 .
0
)
)
)
)
(
x4
(
λ x8 :
(
ι → ι
)
→ ι
.
0
)
Inj1
)
)
)
⟶
False
)
⟶
∀ x0 : ο .
x0
(proof)
Theorem
932cb..
:
(
∀ x0 :
(
ι →
ι → ι
)
→
(
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι → ο
.
∀ x1 :
(
ι → ι
)
→
(
(
ι →
ι →
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ο
.
∀ x2 :
(
ι → ι
)
→
(
ι →
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι →
ι →
ι → ο
.
∀ x3 :
(
(
ι → ι
)
→
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
(
(
ι →
ι → ι
)
→ ι
)
→ ι
)
→
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ο
.
(
∀ x4 :
(
(
ι →
ι → ι
)
→ ι
)
→ ι
.
∀ x5 x6 x7 .
In
(
setsum
x5
(
Inj0
x6
)
)
(
setsum
0
(
x4
(
λ x8 :
ι →
ι → ι
.
Inj0
(
Inj0
0
)
)
)
)
⟶
x0
(
λ x8 x9 .
0
)
(
λ x8 :
ι →
(
ι → ι
)
→
ι → ι
.
0
)
(
setsum
0
(
Inj0
(
setsum
x6
(
Inj0
0
)
)
)
)
⟶
x3
(
λ x8 :
ι → ι
.
λ x9 .
λ x10 :
(
ι → ι
)
→
ι → ι
.
x7
)
(
λ x8 :
(
ι →
ι → ι
)
→ ι
.
x6
)
(
λ x8 :
(
ι → ι
)
→ ι
.
Inj1
0
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 x6 .
∀ x7 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
x3
(
λ x8 :
ι → ι
.
λ x9 .
λ x10 :
(
ι → ι
)
→
ι → ι
.
x9
)
(
λ x8 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x8 :
(
ι → ι
)
→ ι
.
Inj1
x6
)
⟶
In
(
Inj0
0
)
(
setsum
(
setsum
x6
(
setsum
x5
0
)
)
(
Inj0
(
setsum
x6
(
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 :
(
(
ι →
ι → ι
)
→ ι
)
→ ι
.
∀ x5 .
∀ x6 :
(
(
ι →
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→
ι → ι
.
∀ x7 :
(
ι →
ι →
ι → ι
)
→
ι → ι
.
In
(
x4
(
λ x8 :
ι →
ι → ι
.
x7
(
λ x9 x10 x11 .
x10
)
0
)
)
(
Inj1
(
x7
(
λ x8 x9 x10 .
0
)
(
setsum
0
(
Inj0
0
)
)
)
)
⟶
x1
(
λ x8 .
Inj1
(
Inj1
0
)
)
(
λ x8 :
ι →
ι →
ι → ι
.
setsum
0
(
Inj1
(
setsum
(
setsum
0
0
)
(
x8
0
0
0
)
)
)
)
(
λ x8 .
setsum
(
x7
(
λ x9 x10 x11 .
0
)
(
Inj1
x8
)
)
(
Inj1
x8
)
)
(
λ x8 :
ι → ι
.
0
)
(
λ x8 .
x5
)
⟶
x2
(
λ x8 .
setsum
(
setsum
0
(
Inj0
x5
)
)
(
Inj1
0
)
)
(
λ x8 .
λ x9 :
(
ι → ι
)
→ ι
.
Inj1
(
x9
(
λ x10 .
0
)
)
)
(
Inj0
(
x4
(
λ x8 :
ι →
ι → ι
.
0
)
)
)
(
setsum
0
0
)
(
setsum
(
x7
(
λ x8 x9 x10 .
setsum
(
Inj0
0
)
(
setsum
0
0
)
)
(
x6
(
λ x8 :
ι →
ι → ι
.
setsum
0
0
)
(
λ x8 x9 .
x7
(
λ x10 x11 x12 .
0
)
0
)
(
setsum
0
0
)
)
)
(
x4
(
λ x8 :
ι →
ι → ι
.
x7
(
λ x9 x10 x11 .
setsum
0
0
)
(
x6
(
λ x9 :
ι →
ι → ι
.
0
)
(
λ x9 x10 .
0
)
0
)
)
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 .
∀ x6 :
ι → ι
.
∀ x7 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
ι →
ι →
ι → ι
.
In
(
Inj0
(
Inj1
(
setsum
(
x4
0
)
(
setsum
0
0
)
)
)
)
(
Inj0
0
)
⟶
x2
(
λ x8 .
Inj0
(
x7
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 .
setsum
(
Inj1
0
)
0
)
0
(
x6
(
Inj1
0
)
)
0
)
)
(
λ x8 .
λ x9 :
(
ι → ι
)
→ ι
.
0
)
(
Inj1
(
x4
(
Inj0
0
)
)
)
(
x6
(
setsum
(
x7
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
setsum
0
0
)
(
Inj1
0
)
(
x7
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
0
)
0
0
0
)
0
)
(
x7
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
setsum
0
0
)
(
setsum
0
0
)
(
x6
0
)
0
)
)
)
(
setsum
(
x7
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
Inj0
0
)
(
x4
(
x6
0
)
)
(
setsum
(
Inj1
0
)
(
Inj1
0
)
)
0
)
(
Inj0
(
x4
0
)
)
)
⟶
x2
(
λ x8 .
setsum
0
(
Inj0
(
x6
(
setsum
0
0
)
)
)
)
(
λ x8 .
λ x9 :
(
ι → ι
)
→ ι
.
x8
)
(
Inj0
(
x6
(
setsum
0
(
setsum
0
0
)
)
)
)
(
Inj0
x5
)
(
Inj0
(
setsum
x5
(
x4
(
x4
0
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
(
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
)
→
ι →
ι →
ι → ι
.
∀ x6 :
ι →
ι →
ι → ι
.
∀ x7 .
x1
(
λ x8 .
Inj0
(
setsum
(
Inj1
(
Inj1
0
)
)
x8
)
)
(
λ x8 :
ι →
ι →
ι → ι
.
Inj1
(
x5
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 x11 .
0
)
0
0
0
)
)
(
λ x8 .
setsum
0
(
Inj1
(
Inj1
x7
)
)
)
(
λ x8 :
ι → ι
.
0
)
(
λ x8 .
0
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
(
ι → ι
)
→ ι
.
∀ x6 :
ι →
ι → ι
.
∀ x7 :
ι → ι
.
x1
(
λ x8 .
x5
(
Inj1
(
setsum
0
(
Inj1
0
)
)
)
(
λ x9 .
setsum
(
setsum
(
Inj1
0
)
x9
)
x8
)
)
(
λ x8 :
ι →
ι →
ι → ι
.
Inj0
(
Inj0
(
Inj0
(
x7
0
)
)
)
)
(
λ x8 .
Inj1
(
Inj0
(
setsum
(
Inj0
0
)
(
x6
0
0
)
)
)
)
(
λ x8 :
ι → ι
.
x6
(
setsum
(
x6
0
(
setsum
0
0
)
)
(
x6
(
Inj0
0
)
(
x8
0
)
)
)
(
Inj0
(
setsum
(
setsum
0
0
)
(
Inj0
0
)
)
)
)
(
λ x8 .
0
)
⟶
x1
(
λ x8 .
x6
(
Inj1
(
x5
0
(
λ x9 .
x8
)
)
)
0
)
(
λ x8 :
ι →
ι →
ι → ι
.
setsum
(
Inj0
(
Inj0
(
Inj1
0
)
)
)
0
)
(
λ x8 .
Inj0
(
setsum
(
setsum
(
Inj0
0
)
(
x7
0
)
)
0
)
)
(
λ x8 :
ι → ι
.
0
)
(
λ x8 .
0
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x6 x7 .
In
x7
x4
⟶
x0
(
λ x8 .
Inj0
)
(
λ x8 :
ι →
(
ι → ι
)
→
ι → ι
.
Inj0
(
setsum
x7
0
)
)
(
Inj0
(
x5
(
Inj0
x7
)
(
λ x8 x9 .
0
)
(
λ x8 .
0
)
)
)
⟶
x0
(
λ x8 x9 .
Inj0
x8
)
(
λ x8 :
ι →
(
ι → ι
)
→
ι → ι
.
Inj1
x6
)
(
setsum
(
setsum
0
(
Inj1
x6
)
)
(
setsum
(
Inj1
0
)
(
setsum
0
(
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
∀ x6 x7 .
x0
(
λ x8 x9 .
setsum
x7
x6
)
(
λ x8 :
ι →
(
ι → ι
)
→
ι → ι
.
Inj1
(
x8
x7
(
λ x9 .
setsum
x6
(
x8
0
(
λ x10 .
0
)
0
)
)
0
)
)
(
Inj0
(
x4
(
x4
(
Inj1
0
)
)
)
)
⟶
In
(
Inj1
(
setsum
(
x4
(
setsum
0
0
)
)
(
x4
(
setsum
0
0
)
)
)
)
(
Inj1
(
Inj0
0
)
)
)
⟶
False
)
⟶
∀ x0 : ο .
x0
(proof)
Theorem
ca986..
:
(
∀ x0 :
(
(
ι → ι
)
→
ι →
(
ι →
ι → ι
)
→ ι
)
→
ι → ο
.
∀ x1 :
(
ι →
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ο
.
∀ x2 :
(
(
(
ι →
(
ι → ι
)
→ ι
)
→ ι
)
→
(
(
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
ι → ο
.
∀ x3 :
(
(
(
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→ ι
)
→ ι
)
→
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ο
.
(
∀ x4 .
∀ x5 :
ι →
ι → ι
.
∀ x6 .
∀ x7 :
ι → ι
.
x2
(
λ x8 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x10 .
Inj1
0
)
(
Inj1
(
setsum
(
Inj0
0
)
(
x5
0
(
Inj0
0
)
)
)
)
⟶
x3
(
λ x8 :
(
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
x6
)
(
λ x8 :
(
ι → ι
)
→ ι
.
0
)
)
⟶
(
∀ x4 .
∀ x5 x6 :
ι → ι
.
∀ x7 .
x3
(
λ x8 :
(
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
setsum
x7
(
setsum
(
x6
(
setsum
0
0
)
)
0
)
)
(
λ x8 :
(
ι → ι
)
→ ι
.
setsum
(
x8
(
λ x9 .
0
)
)
(
Inj1
(
Inj0
(
Inj0
0
)
)
)
)
⟶
x0
(
λ x8 :
ι → ι
.
λ x9 .
λ x10 :
ι →
ι → ι
.
setsum
0
x7
)
(
setsum
(
Inj1
0
)
(
setsum
(
Inj0
0
)
(
Inj1
(
Inj1
0
)
)
)
)
)
⟶
(
∀ x4 :
(
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x5 :
(
ι →
(
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x6 .
∀ x7 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
In
(
Inj1
(
setsum
0
(
setsum
0
0
)
)
)
(
Inj1
0
)
⟶
x2
(
λ x8 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x10 .
0
)
(
x7
(
λ x8 :
ι →
ι → ι
.
λ x9 :
ι → ι
.
λ x10 .
x8
(
Inj0
(
setsum
0
0
)
)
(
x9
(
setsum
0
0
)
)
)
)
⟶
x2
(
λ x8 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x10 .
setsum
(
setsum
(
setsum
(
x7
(
λ x11 :
ι →
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
0
)
)
(
setsum
0
0
)
)
(
Inj1
(
setsum
0
0
)
)
)
(
x9
(
λ x11 .
setsum
(
Inj1
0
)
(
x8
(
λ x12 .
λ x13 :
ι → ι
.
0
)
)
)
(
λ x11 .
0
)
)
)
(
x4
(
λ x8 x9 :
ι → ι
.
λ x10 .
x8
0
)
)
)
⟶
(
∀ x4 :
(
ι →
(
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→
ι → ι
.
∀ x5 x6 .
∀ x7 :
ι →
ι → ι
.
x2
(
λ x8 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x10 .
0
)
0
⟶
x3
(
λ x8 :
(
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
0
)
(
λ x8 :
(
ι → ι
)
→ ι
.
0
)
)
⟶
(
∀ x4 :
(
ι →
ι →
ι → ι
)
→ ι
.
∀ x5 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
ι →
ι →
ι → ι
.
∀ x6 x7 .
In
(
Inj0
(
x4
(
λ x8 x9 x10 .
0
)
)
)
(
Inj0
0
)
⟶
x2
(
λ x8 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x10 .
Inj1
x7
)
0
⟶
x1
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 .
Inj1
(
x9
x8
)
)
(
λ x8 :
ι → ι
.
Inj1
(
setsum
(
x8
(
setsum
0
0
)
)
(
Inj0
(
Inj0
0
)
)
)
)
(
λ x8 .
Inj1
(
Inj0
0
)
)
(
λ x8 x9 .
0
)
)
⟶
(
∀ x4 .
∀ x5 :
(
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
∀ x6 x7 .
x1
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 .
Inj0
(
x10
(
λ x12 .
0
)
x8
)
)
(
λ x8 :
ι → ι
.
setsum
x7
(
setsum
(
setsum
0
(
setsum
0
0
)
)
x7
)
)
(
λ x8 .
0
)
(
λ x8 x9 .
0
)
⟶
In
(
Inj1
(
setsum
(
x5
(
λ x8 x9 :
ι → ι
.
λ x10 .
Inj0
0
)
x4
(
λ x8 .
setsum
0
0
)
x7
)
(
Inj0
0
)
)
)
(
setsum
(
setsum
x7
(
setsum
0
(
setsum
0
0
)
)
)
(
setsum
(
setsum
(
setsum
0
0
)
x4
)
x6
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 .
∀ x6 :
ι → ι
.
∀ x7 .
In
x7
(
setsum
0
0
)
⟶
x2
(
λ x8 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x10 .
Inj1
(
setsum
0
(
Inj0
0
)
)
)
(
x6
(
setsum
(
setsum
(
x6
0
)
0
)
(
x6
(
Inj1
0
)
)
)
)
⟶
x0
(
λ x8 :
ι → ι
.
λ x9 .
λ x10 :
ι →
ι → ι
.
Inj1
0
)
(
x6
(
Inj0
(
setsum
(
setsum
0
0
)
0
)
)
)
)
⟶
(
∀ x4 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x5 .
∀ x6 :
(
ι → ι
)
→
ι → ι
.
∀ x7 :
(
ι →
ι →
ι → ι
)
→ ι
.
In
(
Inj0
(
Inj1
0
)
)
x5
⟶
x0
(
λ x8 :
ι → ι
.
λ x9 .
λ x10 :
ι →
ι → ι
.
x8
x9
)
(
x4
(
λ x8 .
λ x9 :
ι → ι
.
λ x10 .
0
)
)
⟶
x0
(
λ x8 :
ι → ι
.
λ x9 .
λ x10 :
ι →
ι → ι
.
0
)
0
)
⟶
False
)
⟶
∀ x0 : ο .
x0
(proof)
Theorem
2d8bb..
:
(
∀ x0 :
(
(
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→ ι
)
→
(
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→ ο
.
∀ x1 :
(
(
(
ι →
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
)
→ ο
.
∀ x2 :
(
ι → ι
)
→
ι → ο
.
∀ x3 :
(
ι → ι
)
→
ι →
ι → ο
.
(
∀ x4 :
ι → ι
.
∀ x5 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
.
∀ x6 x7 :
(
ι →
ι → ι
)
→ ι
.
In
(
setsum
(
setsum
(
setsum
(
x4
0
)
(
setsum
0
0
)
)
(
Inj0
0
)
)
(
setsum
(
x6
(
λ x8 x9 .
Inj1
0
)
)
0
)
)
(
Inj1
(
setsum
(
setsum
(
Inj1
0
)
(
setsum
0
0
)
)
0
)
)
⟶
x3
(
λ x8 .
0
)
0
(
setsum
(
setsum
(
x7
(
λ x8 x9 .
setsum
0
0
)
)
0
)
(
Inj1
(
Inj1
(
Inj0
0
)
)
)
)
⟶
x3
(
λ x8 .
setsum
(
Inj1
(
setsum
(
x7
(
λ x9 x10 .
0
)
)
(
setsum
0
0
)
)
)
(
Inj1
(
setsum
0
(
x5
(
λ x9 :
(
ι → ι
)
→ ι
.
0
)
)
)
)
)
(
x4
(
x7
(
λ x8 x9 .
setsum
0
(
Inj1
0
)
)
)
)
0
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 :
(
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
∀ x6 x7 .
In
(
Inj0
0
)
x7
⟶
x3
(
λ x8 .
Inj0
0
)
0
x6
⟶
x3
(
λ x8 .
0
)
(
setsum
0
0
)
(
Inj0
(
Inj1
0
)
)
)
⟶
(
∀ x4 :
(
(
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
∀ x5 .
∀ x6 :
ι → ι
.
∀ x7 .
x1
(
λ x8 :
(
ι →
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x9 .
0
)
(
λ x8 :
ι →
(
ι → ι
)
→ ι
.
setsum
x7
)
⟶
x2
(
λ x8 .
0
)
(
x4
(
λ x8 x9 :
ι → ι
.
Inj1
(
Inj0
0
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x6 :
ι → ι
.
∀ x7 .
In
(
setsum
x4
(
setsum
(
Inj0
(
setsum
0
0
)
)
(
setsum
0
x7
)
)
)
(
Inj1
0
)
⟶
x2
(
λ x8 .
Inj1
(
Inj1
0
)
)
(
setsum
0
x7
)
⟶
x2
(
λ x8 .
x7
)
(
Inj0
(
Inj1
0
)
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x7 .
In
(
Inj1
(
setsum
(
Inj1
0
)
(
Inj1
(
x6
(
λ x8 :
ι → ι
.
0
)
)
)
)
)
(
Inj0
(
setsum
0
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
)
⟶
x2
(
λ x8 .
Inj0
(
x6
(
λ x9 :
ι → ι
.
setsum
(
Inj0
0
)
0
)
)
)
x5
⟶
x1
(
λ x8 :
(
ι →
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x9 .
Inj0
(
Inj0
(
x6
(
λ x10 :
ι → ι
.
x7
)
)
)
)
(
λ x8 :
ι →
(
ι → ι
)
→ ι
.
λ x9 .
setsum
0
(
setsum
(
setsum
(
Inj1
0
)
x9
)
(
Inj0
x7
)
)
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x5 x6 x7 .
x1
(
λ x8 :
(
ι →
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x9 .
setsum
(
setsum
0
(
setsum
x9
0
)
)
0
)
(
λ x8 :
ι →
(
ι → ι
)
→ ι
.
setsum
0
)
⟶
False
)
⟶
(
∀ x4 :
ι →
ι → ι
.
∀ x5 x6 .
∀ x7 :
ι → ι
.
x0
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
setsum
(
Inj0
0
)
x6
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x9 .
0
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→ ι
.
∀ x5 .
∀ x6 :
(
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→
(
ι →
ι → ι
)
→
ι →
ι → ι
.
∀ x7 .
x0
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
x7
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x9 .
x6
(
λ x10 :
ι →
ι → ι
.
λ x11 x12 .
setsum
0
(
setsum
(
Inj0
0
)
(
setsum
0
0
)
)
)
(
λ x10 x11 .
setsum
x9
(
x8
(
λ x12 :
ι → ι
.
setsum
0
0
)
(
λ x12 .
Inj0
0
)
x9
)
)
x9
(
setsum
(
Inj0
0
)
(
Inj0
(
setsum
0
0
)
)
)
)
⟶
x0
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x9 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
setsum
(
x6
(
λ x10 :
ι →
ι → ι
.
λ x11 x12 .
setsum
x12
0
)
(
λ x10 x11 .
x10
)
x7
(
Inj0
(
setsum
0
0
)
)
)
0
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x9 .
setsum
(
setsum
(
setsum
(
setsum
0
0
)
0
)
(
setsum
(
setsum
0
0
)
0
)
)
(
setsum
(
Inj1
(
setsum
0
0
)
)
(
Inj1
(
setsum
0
0
)
)
)
)
)
⟶
False
)
⟶
∀ x0 : ο .
x0
(proof)
Theorem
586ae..
:
(
∀ x0 :
(
ι → ι
)
→
(
ι → ι
)
→
(
ι → ι
)
→
ι →
ι → ο
.
∀ x1 :
(
(
(
ι →
ι →
ι → ι
)
→
ι → ι
)
→
(
(
ι →
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι →
ι → ι
)
→ ο
.
∀ x2 :
(
(
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι → ι
)
→ ι
)
→ ι
)
→
ι → ο
.
∀ x3 :
(
(
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
)
→ ι
)
→
(
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→
ι → ο
.
(
∀ x4 x5 .
∀ x6 :
ι → ι
.
∀ x7 :
ι →
ι → ι
.
In
(
Inj1
(
setsum
x4
(
Inj0
(
Inj0
0
)
)
)
)
x4
⟶
x0
(
λ x8 .
0
)
(
λ x8 .
Inj1
(
Inj1
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
)
(
λ x8 .
setsum
(
setsum
0
x8
)
(
setsum
(
Inj1
(
Inj0
0
)
)
(
Inj0
0
)
)
)
(
setsum
(
Inj1
(
Inj0
(
Inj1
0
)
)
)
x4
)
0
⟶
x3
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
x5
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
x6
(
Inj1
(
x6
0
)
)
)
x5
(
λ x8 .
x8
)
0
)
⟶
(
∀ x4 x5 .
∀ x6 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x7 .
x3
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
Inj0
0
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
x7
)
(
Inj1
(
setsum
(
Inj1
(
Inj1
0
)
)
(
setsum
(
Inj0
0
)
x5
)
)
)
(
λ x8 .
0
)
(
setsum
(
Inj1
(
Inj0
(
Inj1
0
)
)
)
(
Inj0
x7
)
)
⟶
In
(
Inj0
x4
)
x5
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 :
(
(
ι →
ι → ι
)
→ ι
)
→ ι
.
∀ x6 :
(
ι →
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x7 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
In
(
setsum
(
Inj1
(
Inj0
(
x7
(
λ x8 :
(
ι → ι
)
→
ι → ι
.
0
)
)
)
)
0
)
(
Inj1
(
Inj1
0
)
)
⟶
x2
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
0
)
(
Inj1
0
)
⟶
x2
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
x6
(
λ x9 x10 .
0
)
(
λ x9 :
ι → ι
.
λ x10 .
Inj1
(
Inj0
(
Inj0
0
)
)
)
)
(
Inj1
0
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 x6 .
∀ x7 :
ι →
ι → ι
.
x2
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
0
)
0
⟶
x2
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
x5
)
(
Inj0
x5
)
)
⟶
(
∀ x4 :
(
ι →
ι →
ι → ι
)
→
ι →
(
ι → ι
)
→ ι
.
∀ x5 :
(
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
∀ x6 .
∀ x7 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
.
x3
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
setsum
0
0
)
(
λ x8 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
setsum
(
Inj0
(
setsum
(
Inj1
0
)
(
setsum
0
0
)
)
)
(
setsum
(
x7
(
λ x9 :
(
ι → ι
)
→ ι
.
setsum
0
0
)
)
(
setsum
0
0
)
)
)
(
x5
(
λ x8 .
Inj1
(
setsum
(
Inj0
0
)
(
Inj0
0
)
)
)
(
x7
(
λ x8 :
(
ι → ι
)
→ ι
.
Inj0
(
Inj1
0
)
)
)
(
λ x8 .
0
)
(
Inj0
(
Inj0
(
Inj0
0
)
)
)
)
Inj1
(
setsum
(
Inj1
(
x5
(
λ x8 .
x8
)
(
setsum
0
0
)
(
λ x8 .
0
)
0
)
)
(
Inj1
(
Inj1
(
x7
(
λ x8 :
(
ι → ι
)
→ ι
.
0
)
)
)
)
)
⟶
x1
(
λ x8 :
(
ι →
ι →
ι → ι
)
→
ι → ι
.
λ x9 :
(
ι →
ι → ι
)
→
ι → ι
.
0
)
(
λ x8 x9 x10 .
x9
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
∀ x7 .
x1
(
λ x8 :
(
ι →
ι →
ι → ι
)
→
ι → ι
.
λ x9 :
(
ι →
ι → ι
)
→
ι → ι
.
Inj1
(
setsum
(
setsum
0
0
)
(
Inj0
0
)
)
)
(
λ x8 x9 x10 .
setsum
x9
(
Inj0
(
setsum
x8
x8
)
)
)
⟶
In
(
setsum
(
x6
(
λ x8 .
0
)
(
λ x8 :
ι → ι
.
λ x9 .
Inj0
(
setsum
0
0
)
)
x4
)
(
setsum
0
(
Inj1
0
)
)
)
(
Inj1
x7
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 :
ι →
ι →
(
ι → ι
)
→ ι
.
∀ x6 x7 .
In
(
setsum
(
setsum
0
0
)
0
)
(
x5
0
0
(
λ x8 .
setsum
(
Inj0
(
Inj1
0
)
)
0
)
)
⟶
x0
(
λ x8 .
x6
)
(
λ x8 .
0
)
(
λ x8 .
0
)
x7
x7
⟶
x0
(
λ x8 .
Inj0
0
)
(
λ x8 .
Inj1
0
)
(
λ x8 .
setsum
0
(
x5
0
(
setsum
(
setsum
0
0
)
(
Inj1
0
)
)
(
λ x9 .
x8
)
)
)
0
0
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 :
ι →
ι →
ι →
ι → ι
.
∀ x7 .
In
(
setsum
(
x5
(
Inj1
0
)
)
0
)
(
setsum
(
Inj0
x7
)
(
Inj1
(
setsum
x7
(
setsum
0
0
)
)
)
)
⟶
x0
(
λ x8 .
Inj1
0
)
(
λ x8 .
0
)
(
λ x8 .
Inj1
(
x5
0
)
)
(
x5
(
Inj1
0
)
)
0
⟶
x2
(
λ x8 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
setsum
0
(
setsum
(
setsum
0
0
)
(
setsum
(
Inj0
0
)
(
setsum
0
0
)
)
)
)
(
x5
(
setsum
0
x4
)
)
)
⟶
False
)
⟶
∀ x0 : ο .
x0
(proof)
Theorem
f1111..
:
(
∀ x0 :
(
ι → ι
)
→
(
(
ι →
ι →
ι → ι
)
→ ι
)
→ ο
.
∀ x1 :
(
ι → ι
)
→
(
ι → ι
)
→ ο
.
∀ x2 :
(
(
(
(
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→
ι → ι
)
→
ι →
ι →
ι → ι
)
→
ι → ο
.
∀ x3 :
(
ι → ι
)
→
ι → ο
.
(
∀ x4 x5 x6 x7 .
x3
(
λ x8 .
0
)
0
)
⟶
(
∀ x4 .
∀ x5 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x6 .
∀ x7 :
ι → ι
.
In
(
x7
x4
)
(
Inj0
0
)
⟶
x3
(
λ x8 .
x7
x6
)
(
setsum
(
x7
(
setsum
(
setsum
0
0
)
x6
)
)
0
)
⟶
x2
(
λ x8 :
(
(
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
λ x9 x10 x11 .
setsum
(
x8
(
λ x12 x13 :
ι → ι
.
Inj0
0
)
x10
(
λ x12 .
0
)
(
Inj0
(
setsum
0
0
)
)
)
(
setsum
(
setsum
(
Inj0
0
)
(
Inj0
0
)
)
(
Inj1
x11
)
)
)
(
setsum
(
setsum
(
Inj0
(
setsum
0
0
)
)
(
setsum
(
x5
(
λ x8 :
(
ι → ι
)
→ ι
.
0
)
(
λ x8 :
ι → ι
.
λ x9 .
0
)
)
(
setsum
0
0
)
)
)
(
setsum
(
x5
(
λ x8 :
(
ι → ι
)
→ ι
.
Inj1
0
)
(
λ x8 :
ι → ι
.
λ x9 .
x9
)
)
(
Inj1
(
Inj1
0
)
)
)
)
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
x2
(
λ x8 :
(
(
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
λ x9 x10 x11 .
Inj1
(
Inj0
x9
)
)
(
setsum
(
Inj1
(
Inj0
(
setsum
0
0
)
)
)
(
Inj1
(
setsum
(
Inj0
0
)
0
)
)
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
ι → ι
.
∀ x7 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
In
(
Inj0
(
setsum
(
x7
0
(
λ x8 :
ι → ι
.
λ x9 .
0
)
(
setsum
0
0
)
(
x6
0
)
)
(
x6
(
setsum
0
0
)
)
)
)
(
Inj0
(
Inj1
0
)
)
⟶
x2
(
λ x8 :
(
(
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
λ x9 x10 x11 .
0
)
(
setsum
(
x6
(
Inj1
(
x6
0
)
)
)
(
Inj0
(
x7
(
setsum
0
0
)
(
λ x8 :
ι → ι
.
λ x9 .
0
)
x4
(
x7
0
(
λ x8 :
ι → ι
.
λ x9 .
0
)
0
0
)
)
)
)
⟶
x3
(
λ x8 .
setsum
(
setsum
(
x6
(
Inj1
0
)
)
(
x6
x5
)
)
(
x7
(
setsum
(
Inj0
0
)
(
x7
0
(
λ x9 :
ι → ι
.
λ x10 .
0
)
0
0
)
)
(
λ x9 :
ι → ι
.
λ x10 .
Inj0
0
)
(
Inj0
(
x7
0
(
λ x9 :
ι → ι
.
λ x10 .
0
)
0
0
)
)
(
x7
x8
(
λ x9 :
ι → ι
.
λ x10 .
setsum
0
0
)
0
(
Inj1
0
)
)
)
)
(
Inj0
x4
)
)
⟶
(
∀ x4 :
ι →
(
ι →
ι → ι
)
→
ι →
ι → ι
.
∀ x5 :
(
ι →
ι → ι
)
→ ι
.
∀ x6 .
∀ x7 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
.
In
(
Inj1
(
Inj0
0
)
)
(
setsum
(
x4
(
setsum
(
Inj1
0
)
(
setsum
0
0
)
)
(
λ x8 x9 .
x8
)
(
setsum
(
Inj1
0
)
(
x4
0
(
λ x8 x9 .
0
)
0
0
)
)
x6
)
(
setsum
(
x4
(
Inj1
0
)
(
λ x8 x9 .
Inj1
0
)
(
setsum
0
0
)
0
)
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
)
⟶
x0
(
λ x8 .
Inj1
x6
)
(
λ x8 :
ι →
ι →
ι → ι
.
0
)
⟶
x1
(
λ x8 .
Inj1
(
setsum
0
(
setsum
(
x7
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 .
0
)
)
(
x7
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 .
0
)
)
)
)
)
(
λ x8 .
setsum
(
x5
(
λ x9 x10 .
x10
)
)
(
setsum
0
(
Inj1
0
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x6 :
(
(
ι → ι
)
→
ι →
ι → ι
)
→
ι →
ι → ι
.
∀ x7 :
ι →
(
ι →
ι → ι
)
→ ι
.
In
(
x7
(
setsum
0
0
)
(
λ x8 x9 .
Inj1
(
Inj1
0
)
)
)
(
setsum
(
Inj1
x4
)
(
x6
(
λ x8 :
ι → ι
.
λ x9 x10 .
setsum
x9
0
)
(
setsum
(
setsum
0
0
)
(
x6
(
λ x8 :
ι → ι
.
λ x9 x10 .
0
)
0
0
)
)
(
x6
(
λ x8 :
ι → ι
.
λ x9 x10 .
Inj0
0
)
x4
0
)
)
)
⟶
x1
(
λ x8 .
setsum
0
(
setsum
0
(
Inj1
0
)
)
)
(
λ x8 .
setsum
(
x5
0
(
λ x9 :
ι → ι
.
λ x10 .
0
)
)
(
setsum
(
setsum
0
(
setsum
0
0
)
)
(
Inj0
(
Inj1
0
)
)
)
)
⟶
x1
(
λ x8 .
Inj1
(
x6
(
λ x9 :
ι → ι
.
λ x10 x11 .
setsum
(
Inj1
0
)
(
x9
0
)
)
(
Inj0
(
Inj0
0
)
)
(
Inj0
(
x5
0
(
λ x9 :
ι → ι
.
λ x10 .
0
)
)
)
)
)
(
λ x8 .
0
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
∀ x7 :
ι →
ι →
ι → ι
.
In
x4
(
x7
0
(
Inj1
(
setsum
(
Inj0
0
)
(
Inj0
0
)
)
)
x5
)
⟶
x0
(
λ x8 .
setsum
x8
(
setsum
x8
0
)
)
(
λ x8 :
ι →
ι →
ι → ι
.
0
)
⟶
x0
(
λ x8 .
x7
(
setsum
0
0
)
(
setsum
x8
0
)
(
Inj1
0
)
)
(
λ x8 :
ι →
ι →
ι → ι
.
0
)
)
⟶
(
∀ x4 x5 x6 x7 .
x0
(
λ x8 .
setsum
(
setsum
0
0
)
0
)
(
λ x8 :
ι →
ι →
ι → ι
.
setsum
(
setsum
0
0
)
(
setsum
(
Inj1
0
)
0
)
)
⟶
x3
(
λ x8 .
0
)
(
Inj0
(
setsum
(
Inj0
0
)
(
Inj1
(
setsum
0
0
)
)
)
)
)
⟶
False
)
⟶
∀ x0 : ο .
x0
(proof)