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Proofgold Asset
asset id
3d77313f21ab4acbd2a2c7db9e637f96b594d683dccdf73d6c2b7f5a7645950e
asset hash
0aabf178334b95b107a8780d7f5643e949fcc4922ebc8adadaa20d315f1863f9
bday / block
11848
tx
4660d..
preasset
doc published by
PrGVS..
Known
FalseE
FalseE
:
False
⟶
∀ x0 : ο .
x0
Known
notE
notE
:
∀ x0 : ο .
not
x0
⟶
x0
⟶
False
Known
e3ec9..
neq_0_1
:
not
(
0
=
1
)
Theorem
45506..
:
∀ x0 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
∀ x1 :
(
(
(
ι →
ι → ι
)
→ ι
)
→ ι
)
→
(
ι →
(
ι → ι
)
→
ι →
ι → ι
)
→
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
∀ x2 :
(
ι → ι
)
→
ι →
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x3 :
(
ι →
ι → ι
)
→
(
ι →
ι →
(
ι → ι
)
→ ι
)
→ ι
.
(
∀ x4 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x5 :
ι → ι
.
∀ x6 :
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x7 .
x3
(
λ x9 x10 .
x2
(
λ x11 .
0
)
(
x1
(
λ x11 :
(
ι →
ι → ι
)
→ ι
.
x0
(
λ x12 :
ι → ι
.
λ x13 .
x1
(
λ x14 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x14 .
λ x15 :
ι → ι
.
λ x16 x17 .
0
)
(
λ x14 :
(
ι → ι
)
→
ι → ι
.
0
)
)
(
λ x12 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x13 .
x13
)
(
λ x12 :
ι → ι
.
x10
)
0
(
λ x12 .
x10
)
(
Inj0
0
)
)
(
λ x11 .
λ x12 :
ι → ι
.
λ x13 x14 .
Inj0
(
x12
0
)
)
(
λ x11 :
(
ι → ι
)
→
ι → ι
.
0
)
)
(
Inj1
0
)
(
λ x11 :
ι → ι
.
0
)
)
(
λ x9 x10 .
λ x11 :
ι → ι
.
0
)
=
x2
(
λ x9 .
setsum
(
x1
(
λ x10 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x10 .
λ x11 :
ι → ι
.
λ x12 x13 .
0
)
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
x10
(
λ x11 .
0
)
(
Inj0
0
)
)
)
(
x3
(
λ x10 x11 .
x2
(
λ x12 .
setsum
0
0
)
0
(
x0
(
λ x12 :
ι → ι
.
λ x13 .
0
)
(
λ x12 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x13 .
0
)
(
λ x12 :
ι → ι
.
0
)
0
(
λ x12 .
0
)
0
)
(
λ x12 :
ι → ι
.
x2
(
λ x13 .
0
)
0
0
(
λ x13 :
ι → ι
.
0
)
)
)
(
λ x10 x11 .
λ x12 :
ι → ι
.
0
)
)
)
(
x5
(
x5
(
x4
(
λ x9 :
ι →
ι → ι
.
λ x10 :
ι → ι
.
λ x11 .
setsum
0
0
)
)
)
)
(
x4
(
λ x9 :
ι →
ι → ι
.
λ x10 :
ι → ι
.
λ x11 .
0
)
)
(
λ x9 :
ι → ι
.
setsum
x7
(
x9
(
x5
0
)
)
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x5 .
∀ x6 :
ι → ι
.
∀ x7 :
(
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
x3
(
λ x9 x10 .
0
)
(
λ x9 x10 .
λ x11 :
ι → ι
.
Inj1
(
x0
(
λ x12 :
ι → ι
.
λ x13 .
setsum
x13
x10
)
(
λ x12 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x13 .
0
)
(
λ x12 :
ι → ι
.
0
)
(
Inj1
(
x3
(
λ x12 x13 .
0
)
(
λ x12 x13 .
λ x14 :
ι → ι
.
0
)
)
)
(
x0
(
λ x12 :
ι → ι
.
λ x13 .
x0
(
λ x14 :
ι → ι
.
λ x15 .
0
)
(
λ x14 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x15 .
0
)
(
λ x14 :
ι → ι
.
0
)
0
(
λ x14 .
0
)
0
)
(
λ x12 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x13 .
x13
)
(
λ x12 :
ι → ι
.
0
)
(
x1
(
λ x12 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x12 .
λ x13 :
ι → ι
.
λ x14 x15 .
0
)
(
λ x12 :
(
ι → ι
)
→
ι → ι
.
0
)
)
(
λ x12 .
0
)
)
0
)
)
=
x4
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
λ x11 .
setsum
(
setsum
(
x9
(
λ x12 .
x0
(
λ x13 :
ι → ι
.
λ x14 .
0
)
(
λ x13 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x14 .
0
)
(
λ x13 :
ι → ι
.
0
)
0
(
λ x13 .
0
)
0
)
)
0
)
(
setsum
0
x11
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 x6 .
∀ x7 :
(
ι → ι
)
→ ι
.
x2
(
λ x9 .
x5
)
(
Inj0
0
)
(
Inj0
0
)
(
λ x9 :
ι → ι
.
0
)
=
x5
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 :
(
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
∀ x6 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
∀ x7 :
ι → ι
.
x2
(
λ x9 .
0
)
(
x0
(
λ x9 :
ι → ι
.
λ x10 .
0
)
(
λ x9 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
x6
(
x7
(
Inj0
0
)
)
0
(
λ x10 .
x2
(
λ x11 .
Inj0
0
)
(
x2
(
λ x11 .
0
)
0
0
(
λ x11 :
ι → ι
.
0
)
)
x10
(
λ x11 :
ι → ι
.
x10
)
)
)
(
λ x9 :
ι → ι
.
0
)
0
(
λ x9 .
0
)
(
setsum
0
(
x3
(
λ x9 x10 .
0
)
(
λ x9 x10 .
λ x11 :
ι → ι
.
setsum
0
0
)
)
)
)
(
x0
(
λ x9 :
ι → ι
.
λ x10 .
x9
0
)
(
λ x9 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x10 .
0
)
(
λ x9 :
ι → ι
.
Inj1
0
)
(
x3
(
λ x9 .
setsum
(
Inj0
0
)
)
(
λ x9 x10 .
λ x11 :
ι → ι
.
Inj0
(
Inj1
0
)
)
)
(
λ x9 .
Inj0
(
x2
(
λ x10 .
x9
)
0
(
x2
(
λ x10 .
0
)
0
0
(
λ x10 :
ι → ι
.
0
)
)
(
λ x10 :
ι → ι
.
x2
(
λ x11 .
0
)
0
0
(
λ x11 :
ι → ι
.
0
)
)
)
)
0
)
(
λ x9 :
ι → ι
.
0
)
=
x0
(
λ x9 :
ι → ι
.
λ x10 .
setsum
(
x9
(
x7
(
x7
0
)
)
)
(
x0
(
λ x11 :
ι → ι
.
λ x12 .
x3
(
λ x13 x14 .
0
)
(
λ x13 x14 .
λ x15 :
ι → ι
.
setsum
0
0
)
)
(
λ x11 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x12 .
x9
(
setsum
0
0
)
)
(
λ x11 :
ι → ι
.
0
)
(
x7
x10
)
(
λ x11 .
x1
(
λ x12 :
(
ι →
ι → ι
)
→ ι
.
x12
(
λ x13 x14 .
0
)
)
(
λ x12 .
λ x13 :
ι → ι
.
λ x14 x15 .
setsum
0
0
)
(
λ x12 :
(
ι → ι
)
→
ι → ι
.
x12
(
λ x13 .
0
)
0
)
)
(
Inj0
0
)
)
)
(
λ x9 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x10 .
x7
(
x6
(
x3
(
λ x11 x12 .
0
)
(
λ x11 x12 .
λ x13 :
ι → ι
.
0
)
)
(
x1
(
λ x11 :
(
ι →
ι → ι
)
→ ι
.
x0
(
λ x12 :
ι → ι
.
λ x13 .
0
)
(
λ x12 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x13 .
0
)
(
λ x12 :
ι → ι
.
0
)
0
(
λ x12 .
0
)
0
)
(
λ x11 .
λ x12 :
ι → ι
.
λ x13 x14 .
Inj1
0
)
(
λ x11 :
(
ι → ι
)
→
ι → ι
.
0
)
)
(
λ x11 .
0
)
(
x0
(
λ x11 :
ι → ι
.
λ x12 .
0
)
(
λ x11 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x12 .
setsum
0
0
)
(
λ x11 :
ι → ι
.
x10
)
(
setsum
0
0
)
(
λ x11 .
setsum
0
0
)
(
Inj0
0
)
)
)
)
(
λ x9 :
ι → ι
.
x9
(
x0
(
λ x10 :
ι → ι
.
λ x11 .
Inj1
(
x0
(
λ x12 :
ι → ι
.
λ x13 .
0
)
(
λ x12 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x13 .
0
)
(
λ x12 :
ι → ι
.
0
)
0
(
λ x12 .
0
)
0
)
)
(
λ x10 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x11 .
x0
(
λ x12 :
ι → ι
.
λ x13 .
0
)
(
λ x12 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x13 .
x2
(
λ x14 .
0
)
0
0
(
λ x14 :
ι → ι
.
0
)
)
(
λ x12 :
ι → ι
.
Inj1
0
)
0
(
λ x12 .
setsum
0
0
)
(
x7
0
)
)
(
λ x10 :
ι → ι
.
x9
(
x3
(
λ x11 x12 .
0
)
(
λ x11 x12 .
λ x13 :
ι → ι
.
0
)
)
)
0
(
λ x10 .
0
)
(
x0
(
λ x10 :
ι → ι
.
λ x11 .
x10
0
)
(
λ x10 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x11 .
0
)
(
λ x10 :
ι → ι
.
Inj0
0
)
(
Inj0
0
)
(
λ x10 .
0
)
(
x6
0
0
(
λ x10 .
0
)
0
)
)
)
)
(
x6
0
(
setsum
(
setsum
0
(
x3
(
λ x9 x10 .
0
)
(
λ x9 x10 .
λ x11 :
ι → ι
.
0
)
)
)
(
x3
(
λ x9 x10 .
setsum
0
0
)
(
λ x9 x10 .
λ x11 :
ι → ι
.
x10
)
)
)
(
λ x9 .
x0
(
λ x10 :
ι → ι
.
λ x11 .
x9
)
(
λ x10 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x11 .
Inj0
0
)
(
λ x10 :
ι → ι
.
x1
(
λ x11 :
(
ι →
ι → ι
)
→ ι
.
Inj0
0
)
(
λ x11 .
λ x12 :
ι → ι
.
λ x13 x14 .
x2
(
λ x15 .
0
)
0
0
(
λ x15 :
ι → ι
.
0
)
)
(
λ x11 :
(
ι → ι
)
→
ι → ι
.
0
)
)
(
Inj1
(
x1
(
λ x10 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x10 .
λ x11 :
ι → ι
.
λ x12 x13 .
0
)
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
0
)
)
)
(
λ x10 .
0
)
(
Inj0
0
)
)
(
Inj0
(
setsum
(
x7
0
)
0
)
)
)
(
λ x9 .
x3
(
λ x10 x11 .
0
)
(
λ x10 x11 .
λ x12 :
ι → ι
.
setsum
(
x1
(
λ x13 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x13 .
λ x14 :
ι → ι
.
λ x15 x16 .
x0
(
λ x17 :
ι → ι
.
λ x18 .
0
)
(
λ x17 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x18 .
0
)
(
λ x17 :
ι → ι
.
0
)
0
(
λ x17 .
0
)
0
)
(
λ x13 :
(
ι → ι
)
→
ι → ι
.
setsum
0
0
)
)
0
)
)
(
Inj0
(
Inj1
(
x6
(
x0
(
λ x9 :
ι → ι
.
λ x10 .
0
)
(
λ x9 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x10 .
0
)
(
λ x9 :
ι → ι
.
0
)
0
(
λ x9 .
0
)
0
)
0
(
λ x9 .
x3
(
λ x10 x11 .
0
)
(
λ x10 x11 .
λ x12 :
ι → ι
.
0
)
)
0
)
)
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x7 :
ι → ι
.
x1
(
λ x9 :
(
ι →
ι → ι
)
→ ι
.
setsum
(
x3
(
λ x10 x11 .
setsum
0
(
x3
(
λ x12 x13 .
0
)
(
λ x12 x13 .
λ x14 :
ι → ι
.
0
)
)
)
(
λ x10 x11 .
λ x12 :
ι → ι
.
0
)
)
(
x7
(
x3
(
λ x10 x11 .
x7
0
)
(
λ x10 x11 .
λ x12 :
ι → ι
.
x3
(
λ x13 x14 .
0
)
(
λ x13 x14 .
λ x15 :
ι → ι
.
0
)
)
)
)
)
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 x12 .
0
)
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
x7
(
x3
(
λ x10 x11 .
Inj1
(
setsum
0
0
)
)
(
λ x10 x11 .
λ x12 :
ι → ι
.
0
)
)
)
=
x7
(
Inj1
x4
)
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
ι →
(
ι → ι
)
→ ι
.
x1
(
λ x9 :
(
ι →
ι → ι
)
→ ι
.
x0
(
λ x10 :
ι → ι
.
λ x11 .
0
)
(
λ x10 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x11 .
0
)
(
λ x10 :
ι → ι
.
x0
(
λ x11 :
ι → ι
.
λ x12 .
x11
(
Inj0
0
)
)
(
λ x11 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x12 .
x3
(
λ x13 x14 .
0
)
(
λ x13 x14 .
λ x15 :
ι → ι
.
0
)
)
(
λ x11 :
ι → ι
.
Inj1
(
x9
(
λ x12 x13 .
0
)
)
)
(
setsum
0
0
)
(
λ x11 .
0
)
(
x9
(
λ x11 x12 .
0
)
)
)
(
x9
(
λ x10 x11 .
x10
)
)
(
λ x10 .
x7
(
x1
(
λ x11 :
(
ι →
ι → ι
)
→ ι
.
Inj1
0
)
(
λ x11 .
λ x12 :
ι → ι
.
λ x13 x14 .
x12
0
)
(
λ x11 :
(
ι → ι
)
→
ι → ι
.
x1
(
λ x12 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x12 .
λ x13 :
ι → ι
.
λ x14 x15 .
0
)
(
λ x12 :
(
ι → ι
)
→
ι → ι
.
0
)
)
)
(
λ x11 .
0
)
)
x5
)
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 x12 .
x11
)
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
x1
(
λ x10 :
(
ι →
ι → ι
)
→ ι
.
x10
(
λ x11 x12 .
setsum
x12
(
x3
(
λ x13 x14 .
0
)
(
λ x13 x14 .
λ x15 :
ι → ι
.
0
)
)
)
)
(
λ x10 .
λ x11 :
ι → ι
.
λ x12 x13 .
x2
(
λ x14 .
setsum
x13
0
)
(
x3
(
λ x14 x15 .
setsum
0
0
)
(
λ x14 x15 .
λ x16 :
ι → ι
.
Inj0
0
)
)
0
(
λ x14 :
ι → ι
.
0
)
)
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
x7
(
x10
(
λ x11 .
0
)
(
x2
(
λ x11 .
0
)
0
0
(
λ x11 :
ι → ι
.
0
)
)
)
(
λ x11 .
setsum
(
x10
(
λ x12 .
0
)
0
)
(
x7
0
(
λ x12 .
0
)
)
)
)
)
=
x1
(
λ x9 :
(
ι →
ι → ι
)
→ ι
.
x3
(
λ x10 x11 .
0
)
(
λ x10 x11 .
λ x12 :
ι → ι
.
x2
(
λ x13 .
x12
x10
)
(
x3
(
λ x13 x14 .
setsum
0
0
)
(
λ x13 x14 .
λ x15 :
ι → ι
.
Inj1
0
)
)
(
Inj1
(
x9
(
λ x13 x14 .
0
)
)
)
(
λ x13 :
ι → ι
.
0
)
)
)
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 x12 .
x1
(
λ x13 :
(
ι →
ι → ι
)
→ ι
.
x10
(
Inj0
0
)
)
(
λ x13 .
λ x14 :
ι → ι
.
λ x15 x16 .
x13
)
(
λ x13 :
(
ι → ι
)
→
ι → ι
.
x2
(
λ x14 .
setsum
(
Inj0
0
)
(
x13
(
λ x15 .
0
)
0
)
)
0
(
x10
(
x0
(
λ x14 :
ι → ι
.
λ x15 .
0
)
(
λ x14 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x15 .
0
)
(
λ x14 :
ι → ι
.
0
)
0
(
λ x14 .
0
)
0
)
)
(
λ x14 :
ι → ι
.
x12
)
)
)
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
x3
(
λ x10 x11 .
0
)
(
λ x10 x11 .
λ x12 :
ι → ι
.
0
)
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x5 :
(
ι → ι
)
→
ι → ι
.
∀ x6 :
ι → ι
.
∀ x7 :
(
(
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
ι →
ι →
ι → ι
.
x0
(
λ x9 :
ι → ι
.
λ x10 .
setsum
(
Inj1
(
Inj1
0
)
)
(
x0
(
λ x11 :
ι → ι
.
λ x12 .
0
)
(
λ x11 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x12 .
0
)
(
λ x11 :
ι → ι
.
x3
(
λ x12 x13 .
0
)
(
λ x12 x13 .
λ x14 :
ι → ι
.
x3
(
λ x15 x16 .
0
)
(
λ x15 x16 .
λ x17 :
ι → ι
.
0
)
)
)
0
(
λ x11 .
x11
)
(
setsum
0
(
Inj0
0
)
)
)
)
(
λ x9 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x10 .
setsum
(
x7
(
λ x11 x12 :
ι → ι
.
Inj1
(
Inj1
0
)
)
(
x6
(
x0
(
λ x11 :
ι → ι
.
λ x12 .
0
)
(
λ x11 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x12 .
0
)
(
λ x11 :
ι → ι
.
0
)
0
(
λ x11 .
0
)
0
)
)
(
setsum
(
setsum
0
0
)
0
)
(
x2
(
λ x11 .
x11
)
(
x9
(
λ x11 :
ι → ι
.
λ x12 .
0
)
(
λ x11 .
0
)
)
(
setsum
0
0
)
(
λ x11 :
ι → ι
.
0
)
)
)
(
x1
(
λ x11 :
(
ι →
ι → ι
)
→ ι
.
x7
(
λ x12 x13 :
ι → ι
.
x10
)
(
x1
(
λ x12 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x12 .
λ x13 :
ι → ι
.
λ x14 x15 .
0
)
(
λ x12 :
(
ι → ι
)
→
ι → ι
.
0
)
)
(
setsum
0
0
)
x10
)
(
λ x11 .
λ x12 :
ι → ι
.
λ x13 x14 .
x11
)
(
λ x11 :
(
ι → ι
)
→
ι → ι
.
Inj0
0
)
)
)
(
λ x9 :
ι → ι
.
x9
(
x7
(
λ x10 x11 :
ι → ι
.
setsum
(
x10
0
)
0
)
(
x9
0
)
(
x3
(
λ x10 x11 .
x9
0
)
(
λ x10 x11 .
λ x12 :
ι → ι
.
0
)
)
(
x9
0
)
)
)
(
x4
(
λ x9 :
(
ι → ι
)
→ ι
.
x9
(
λ x10 .
x7
(
λ x11 x12 :
ι → ι
.
x3
(
λ x13 x14 .
0
)
(
λ x13 x14 .
λ x15 :
ι → ι
.
0
)
)
(
setsum
0
0
)
0
(
x9
(
λ x11 .
0
)
)
)
)
(
λ x9 :
ι → ι
.
setsum
0
(
setsum
0
0
)
)
)
(
λ x9 .
0
)
(
x1
(
λ x9 :
(
ι →
ι → ι
)
→ ι
.
x1
(
λ x10 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x10 .
λ x11 :
ι → ι
.
λ x12 x13 .
Inj0
(
Inj0
0
)
)
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
Inj1
0
)
)
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 x12 .
x1
(
λ x13 :
(
ι →
ι → ι
)
→ ι
.
x3
(
λ x14 x15 .
x1
(
λ x16 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x16 .
λ x17 :
ι → ι
.
λ x18 x19 .
0
)
(
λ x16 :
(
ι → ι
)
→
ι → ι
.
0
)
)
(
λ x14 x15 .
λ x16 :
ι → ι
.
x0
(
λ x17 :
ι → ι
.
λ x18 .
0
)
(
λ x17 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x18 .
0
)
(
λ x17 :
ι → ι
.
0
)
0
(
λ x17 .
0
)
0
)
)
(
λ x13 .
λ x14 :
ι → ι
.
λ x15 x16 .
x2
(
λ x17 .
0
)
x15
0
(
λ x17 :
ι → ι
.
setsum
0
0
)
)
(
λ x13 :
(
ι → ι
)
→
ι → ι
.
x10
(
setsum
0
0
)
)
)
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
x7
(
λ x10 x11 :
ι → ι
.
x7
(
λ x12 x13 :
ι → ι
.
x1
(
λ x14 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x14 .
λ x15 :
ι → ι
.
λ x16 x17 .
0
)
(
λ x14 :
(
ι → ι
)
→
ι → ι
.
0
)
)
(
x2
(
λ x12 .
0
)
0
0
(
λ x12 :
ι → ι
.
0
)
)
(
x2
(
λ x12 .
0
)
0
0
(
λ x12 :
ι → ι
.
0
)
)
0
)
0
(
setsum
(
x2
(
λ x10 .
0
)
0
0
(
λ x10 :
ι → ι
.
0
)
)
(
setsum
0
0
)
)
(
setsum
(
Inj1
0
)
(
x7
(
λ x10 x11 :
ι → ι
.
0
)
0
0
0
)
)
)
)
=
x4
(
λ x9 :
(
ι → ι
)
→ ι
.
setsum
(
setsum
(
x0
(
λ x10 :
ι → ι
.
λ x11 .
x0
(
λ x12 :
ι → ι
.
λ x13 .
0
)
(
λ x12 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x13 .
0
)
(
λ x12 :
ι → ι
.
0
)
0
(
λ x12 .
0
)
0
)
(
λ x10 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x11 .
x3
(
λ x12 x13 .
0
)
(
λ x12 x13 .
λ x14 :
ι → ι
.
0
)
)
(
λ x10 :
ι → ι
.
0
)
(
Inj1
0
)
(
λ x10 .
x9
(
λ x11 .
0
)
)
0
)
0
)
(
x5
(
λ x10 .
x7
(
λ x11 x12 :
ι → ι
.
x10
)
(
setsum
0
0
)
0
(
Inj0
0
)
)
(
setsum
0
(
Inj0
0
)
)
)
)
(
λ x9 :
ι → ι
.
x2
(
λ x10 .
x2
(
λ x11 .
Inj1
0
)
(
Inj1
(
Inj1
0
)
)
(
x9
(
x0
(
λ x11 :
ι → ι
.
λ x12 .
0
)
(
λ x11 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x12 .
0
)
(
λ x11 :
ι → ι
.
0
)
0
(
λ x11 .
0
)
0
)
)
(
λ x11 :
ι → ι
.
setsum
(
x9
0
)
(
x9
0
)
)
)
0
0
(
λ x10 :
ι → ι
.
x2
(
λ x11 .
x2
(
λ x12 .
x10
0
)
0
(
x1
(
λ x12 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x12 .
λ x13 :
ι → ι
.
λ x14 x15 .
0
)
(
λ x12 :
(
ι → ι
)
→
ι → ι
.
0
)
)
(
λ x12 :
ι → ι
.
Inj1
0
)
)
(
x6
(
setsum
0
0
)
)
(
x9
(
Inj0
0
)
)
(
λ x11 :
ι → ι
.
setsum
0
0
)
)
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι → ι
.
∀ x5 :
ι → ι
.
∀ x6 x7 .
x0
(
λ x9 :
ι → ι
.
λ x10 .
x3
(
λ x11 x12 .
x9
(
Inj1
0
)
)
(
λ x11 x12 .
λ x13 :
ι → ι
.
x3
(
λ x14 x15 .
Inj0
(
x0
(
λ x16 :
ι → ι
.
λ x17 .
0
)
(
λ x16 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x17 .
0
)
(
λ x16 :
ι → ι
.
0
)
0
(
λ x16 .
0
)
0
)
)
(
λ x14 x15 .
λ x16 :
ι → ι
.
x16
(
setsum
0
0
)
)
)
)
(
λ x9 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x10 .
x6
)
(
λ x9 :
ι → ι
.
x0
(
λ x10 :
ι → ι
.
λ x11 .
0
)
(
λ x10 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x11 .
x2
(
λ x12 .
x10
(
λ x13 :
ι → ι
.
λ x14 .
setsum
0
0
)
(
λ x13 .
x1
(
λ x14 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x14 .
λ x15 :
ι → ι
.
λ x16 x17 .
0
)
(
λ x14 :
(
ι → ι
)
→
ι → ι
.
0
)
)
)
(
x10
(
λ x12 :
ι → ι
.
λ x13 .
x0
(
λ x14 :
ι → ι
.
λ x15 .
0
)
(
λ x14 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x15 .
0
)
(
λ x14 :
ι → ι
.
0
)
0
(
λ x14 .
0
)
0
)
(
λ x12 .
x10
(
λ x13 :
ι → ι
.
λ x14 .
0
)
(
λ x13 .
0
)
)
)
(
x3
(
λ x12 x13 .
setsum
0
0
)
(
λ x12 x13 .
λ x14 :
ι → ι
.
x2
(
λ x15 .
0
)
0
0
(
λ x15 :
ι → ι
.
0
)
)
)
(
λ x12 :
ι → ι
.
setsum
0
0
)
)
(
λ x10 :
ι → ι
.
x3
(
λ x11 x12 .
Inj0
0
)
(
λ x11 x12 .
λ x13 :
ι → ι
.
0
)
)
(
x9
(
x0
(
λ x10 :
ι → ι
.
λ x11 .
0
)
(
λ x10 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x11 .
0
)
(
λ x10 :
ι → ι
.
x0
(
λ x11 :
ι → ι
.
λ x12 .
0
)
(
λ x11 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x12 .
0
)
(
λ x11 :
ι → ι
.
0
)
0
(
λ x11 .
0
)
0
)
0
(
λ x10 .
0
)
(
x1
(
λ x10 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x10 .
λ x11 :
ι → ι
.
λ x12 x13 .
0
)
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
0
)
)
)
)
(
λ x10 .
x0
(
λ x11 :
ι → ι
.
λ x12 .
x0
(
λ x13 :
ι → ι
.
λ x14 .
Inj0
0
)
(
λ x13 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x14 .
0
)
(
λ x13 :
ι → ι
.
Inj1
0
)
(
x2
(
λ x13 .
0
)
0
0
(
λ x13 :
ι → ι
.
0
)
)
(
λ x13 .
x3
(
λ x14 x15 .
0
)
(
λ x14 x15 .
λ x16 :
ι → ι
.
0
)
)
0
)
(
λ x11 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x12 .
0
)
(
λ x11 :
ι → ι
.
x9
(
x11
0
)
)
0
(
λ x11 .
0
)
(
x3
(
λ x11 x12 .
setsum
0
0
)
(
λ x11 x12 .
λ x13 :
ι → ι
.
setsum
0
0
)
)
)
(
Inj0
x6
)
)
(
Inj0
x7
)
(
λ x9 .
x2
(
λ x10 .
0
)
0
0
(
λ x10 :
ι → ι
.
setsum
(
x0
(
λ x11 :
ι → ι
.
λ x12 .
0
)
(
λ x11 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x12 .
0
)
(
λ x11 :
ι → ι
.
x10
0
)
(
x10
0
)
(
λ x11 .
x10
0
)
(
Inj0
0
)
)
(
Inj0
0
)
)
)
0
=
setsum
(
setsum
(
x4
(
λ x9 :
(
ι → ι
)
→ ι
.
x3
(
λ x10 x11 .
x7
)
(
λ x10 x11 .
λ x12 :
ι → ι
.
Inj0
0
)
)
0
)
(
setsum
(
x0
(
λ x9 :
ι → ι
.
λ x10 .
x3
(
λ x11 x12 .
0
)
(
λ x11 x12 .
λ x13 :
ι → ι
.
0
)
)
(
λ x9 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x10 .
0
)
(
λ x9 :
ι → ι
.
x0
(
λ x10 :
ι → ι
.
λ x11 .
0
)
(
λ x10 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x11 .
0
)
(
λ x10 :
ι → ι
.
0
)
0
(
λ x10 .
0
)
0
)
x6
(
λ x9 .
x9
)
(
x1
(
λ x9 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 x12 .
0
)
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
0
)
)
)
(
Inj1
(
x5
0
)
)
)
)
(
x1
(
λ x9 :
(
ι →
ι → ι
)
→ ι
.
x5
(
x9
(
λ x10 x11 .
x1
(
λ x12 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x12 .
λ x13 :
ι → ι
.
λ x14 x15 .
0
)
(
λ x12 :
(
ι → ι
)
→
ι → ι
.
0
)
)
)
)
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 x12 .
x10
(
Inj1
(
x10
0
)
)
)
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
setsum
x6
(
setsum
(
x9
(
λ x10 .
0
)
0
)
(
x0
(
λ x10 :
ι → ι
.
λ x11 .
0
)
(
λ x10 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x11 .
0
)
(
λ x10 :
ι → ι
.
0
)
0
(
λ x10 .
0
)
0
)
)
)
)
)
⟶
False
(proof)
Theorem
b6398..
:
∀ x0 :
(
ι →
(
(
ι →
ι → ι
)
→ ι
)
→ ι
)
→
(
ι → ι
)
→
(
ι → ι
)
→
ι →
ι →
ι → ι
.
∀ x1 :
(
(
ι →
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι →
ι →
ι → ι
)
→ ι
.
∀ x2 :
(
(
(
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι →
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
∀ x3 :
(
(
(
ι →
ι → ι
)
→ ι
)
→
ι →
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
.
(
∀ x4 x5 x6 .
∀ x7 :
(
ι → ι
)
→
ι →
(
ι → ι
)
→ ι
.
x3
(
λ x9 :
(
ι →
ι → ι
)
→ ι
.
λ x10 x11 .
λ x12 :
ι → ι
.
x2
(
λ x13 x14 :
(
ι → ι
)
→ ι
.
setsum
(
setsum
0
0
)
x11
)
(
λ x13 .
λ x14 :
ι → ι
.
x1
(
λ x15 :
ι →
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
Inj1
(
x0
(
λ x16 .
λ x17 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x16 .
0
)
(
λ x16 .
0
)
0
0
0
)
)
(
λ x15 x16 x17 x18 .
x18
)
)
(
x1
(
λ x13 :
ι →
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x13 x14 x15 x16 .
x16
)
)
(
x0
(
λ x13 .
λ x14 :
(
ι →
ι → ι
)
→ ι
.
x14
(
λ x15 x16 .
x15
)
)
(
λ x13 .
x11
)
(
λ x13 .
x3
(
λ x14 :
(
ι →
ι → ι
)
→ ι
.
λ x15 x16 .
λ x17 :
ι → ι
.
0
)
(
x3
(
λ x14 :
(
ι →
ι → ι
)
→ ι
.
λ x15 x16 .
λ x17 :
ι → ι
.
0
)
0
)
)
(
setsum
0
(
x12
0
)
)
(
x9
(
λ x13 x14 .
x2
(
λ x15 x16 :
(
ι → ι
)
→ ι
.
0
)
(
λ x15 .
λ x16 :
ι → ι
.
0
)
0
0
)
)
(
x3
(
λ x13 :
(
ι →
ι → ι
)
→ ι
.
λ x14 x15 .
λ x16 :
ι → ι
.
x14
)
(
Inj1
0
)
)
)
)
(
setsum
(
x2
(
λ x9 x10 :
(
ι → ι
)
→ ι
.
x9
(
λ x11 .
setsum
0
0
)
)
(
λ x9 .
λ x10 :
ι → ι
.
x0
(
λ x11 .
λ x12 :
(
ι →
ι → ι
)
→ ι
.
x3
(
λ x13 :
(
ι →
ι → ι
)
→ ι
.
λ x14 x15 .
λ x16 :
ι → ι
.
0
)
0
)
(
λ x11 .
x9
)
(
λ x11 .
x2
(
λ x12 x13 :
(
ι → ι
)
→ ι
.
0
)
(
λ x12 .
λ x13 :
ι → ι
.
0
)
0
0
)
(
x10
0
)
(
setsum
0
0
)
0
)
x6
(
setsum
(
Inj0
0
)
0
)
)
x4
)
=
x2
(
λ x9 x10 :
(
ι → ι
)
→ ι
.
x0
(
λ x11 .
λ x12 :
(
ι →
ι → ι
)
→ ι
.
setsum
(
setsum
(
x12
(
λ x13 x14 .
0
)
)
(
x12
(
λ x13 x14 .
0
)
)
)
0
)
(
λ x11 .
0
)
(
λ x11 .
Inj0
(
x7
(
λ x12 .
x11
)
(
x9
(
λ x12 .
0
)
)
(
λ x12 .
Inj0
0
)
)
)
0
0
0
)
(
λ x9 .
λ x10 :
ι → ι
.
x7
(
λ x11 .
x1
(
λ x12 :
ι →
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
Inj0
(
x2
(
λ x13 x14 :
(
ι → ι
)
→ ι
.
0
)
(
λ x13 .
λ x14 :
ι → ι
.
0
)
0
0
)
)
(
λ x12 x13 x14 x15 .
setsum
(
x0
(
λ x16 .
λ x17 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x16 .
0
)
(
λ x16 .
0
)
0
0
0
)
(
setsum
0
0
)
)
)
(
Inj1
x6
)
(
λ x11 .
x10
(
x10
(
x10
0
)
)
)
)
(
x0
(
λ x9 .
λ x10 :
(
ι →
ι → ι
)
→ ι
.
setsum
(
x2
(
λ x11 x12 :
(
ι → ι
)
→ ι
.
x11
(
λ x13 .
0
)
)
(
λ x11 .
λ x12 :
ι → ι
.
Inj0
0
)
(
x10
(
λ x11 x12 .
0
)
)
(
Inj1
0
)
)
(
x0
(
λ x11 .
λ x12 :
(
ι →
ι → ι
)
→ ι
.
Inj0
0
)
(
λ x11 .
0
)
(
λ x11 .
x7
(
λ x12 .
0
)
0
(
λ x12 .
0
)
)
x9
0
(
Inj0
0
)
)
)
(
λ x9 .
x3
(
λ x10 :
(
ι →
ι → ι
)
→ ι
.
λ x11 x12 .
λ x13 :
ι → ι
.
0
)
(
x2
(
λ x10 x11 :
(
ι → ι
)
→ ι
.
x7
(
λ x12 .
0
)
0
(
λ x12 .
0
)
)
(
λ x10 .
λ x11 :
ι → ι
.
x11
0
)
0
0
)
)
Inj0
0
x6
(
x2
(
λ x9 x10 :
(
ι → ι
)
→ ι
.
x7
(
λ x11 .
x1
(
λ x12 :
ι →
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x12 x13 x14 x15 .
0
)
)
0
(
λ x11 .
0
)
)
(
λ x9 .
λ x10 :
ι → ι
.
0
)
0
0
)
)
x4
)
⟶
(
∀ x4 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
∀ x5 .
∀ x6 :
(
ι →
ι → ι
)
→ ι
.
∀ x7 :
(
ι → ι
)
→
ι → ι
.
x3
(
λ x9 :
(
ι →
ι → ι
)
→ ι
.
λ x10 x11 .
λ x12 :
ι → ι
.
x1
(
λ x13 :
ι →
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x13 x14 x15 x16 .
0
)
)
(
x6
(
λ x9 x10 .
0
)
)
=
x6
(
λ x9 x10 .
Inj1
0
)
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
ι → ι
.
x2
(
λ x9 x10 :
(
ι → ι
)
→ ι
.
0
)
(
λ x9 .
λ x10 :
ι → ι
.
0
)
0
0
=
Inj0
x5
)
⟶
(
∀ x4 .
∀ x5 :
(
ι →
ι →
ι → ι
)
→
ι → ι
.
∀ x6 :
(
ι → ι
)
→ ι
.
∀ x7 .
x2
(
λ x9 x10 :
(
ι → ι
)
→ ι
.
x9
(
λ x11 .
x1
(
λ x12 :
ι →
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
x11
)
(
λ x12 x13 x14 x15 .
x15
)
)
)
(
λ x9 .
λ x10 :
ι → ι
.
0
)
0
(
x1
(
λ x9 :
ι →
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
setsum
(
setsum
(
setsum
0
0
)
x7
)
(
Inj1
0
)
)
(
λ x9 x10 x11 x12 .
Inj0
(
x2
(
λ x13 x14 :
(
ι → ι
)
→ ι
.
Inj1
0
)
(
λ x13 .
λ x14 :
ι → ι
.
0
)
(
setsum
0
0
)
(
x2
(
λ x13 x14 :
(
ι → ι
)
→ ι
.
0
)
(
λ x13 .
λ x14 :
ι → ι
.
0
)
0
0
)
)
)
)
=
Inj1
(
Inj0
(
Inj1
(
setsum
(
Inj0
0
)
(
x3
(
λ x9 :
(
ι →
ι → ι
)
→ ι
.
λ x10 x11 .
λ x12 :
ι → ι
.
0
)
0
)
)
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x6 :
(
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x7 .
x1
(
λ x9 :
ι →
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
x9
0
(
λ x10 .
setsum
(
x6
(
λ x11 x12 :
ι → ι
.
λ x13 .
x2
(
λ x14 x15 :
(
ι → ι
)
→ ι
.
0
)
(
λ x14 .
λ x15 :
ι → ι
.
0
)
0
0
)
)
(
x2
(
λ x11 x12 :
(
ι → ι
)
→ ι
.
x10
)
(
λ x11 .
λ x12 :
ι → ι
.
0
)
0
(
x3
(
λ x11 :
(
ι →
ι → ι
)
→ ι
.
λ x12 x13 .
λ x14 :
ι → ι
.
0
)
0
)
)
)
(
λ x10 .
0
)
(
x3
(
λ x10 :
(
ι →
ι → ι
)
→ ι
.
λ x11 x12 .
λ x13 :
ι → ι
.
x1
(
λ x14 :
ι →
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
Inj0
0
)
(
λ x14 x15 x16 x17 .
x2
(
λ x18 x19 :
(
ι → ι
)
→ ι
.
0
)
(
λ x18 .
λ x19 :
ι → ι
.
0
)
0
0
)
)
x7
)
)
(
λ x9 x10 x11 x12 .
Inj0
(
x2
(
λ x13 x14 :
(
ι → ι
)
→ ι
.
0
)
(
λ x13 .
λ x14 :
ι → ι
.
Inj0
x13
)
(
x0
(
λ x13 .
λ x14 :
(
ι →
ι → ι
)
→ ι
.
x2
(
λ x15 x16 :
(
ι → ι
)
→ ι
.
0
)
(
λ x15 .
λ x16 :
ι → ι
.
0
)
0
0
)
(
λ x13 .
x10
)
(
λ x13 .
x1
(
λ x14 :
ι →
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x14 x15 x16 x17 .
0
)
)
(
x1
(
λ x13 :
ι →
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x13 x14 x15 x16 .
0
)
)
(
x0
(
λ x13 .
λ x14 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x13 .
0
)
(
λ x13 .
0
)
0
0
0
)
0
)
(
x2
(
λ x13 x14 :
(
ι → ι
)
→ ι
.
x3
(
λ x15 :
(
ι →
ι → ι
)
→ ι
.
λ x16 x17 .
λ x18 :
ι → ι
.
0
)
0
)
(
λ x13 .
λ x14 :
ι → ι
.
setsum
0
0
)
(
x1
(
λ x13 :
ι →
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x13 x14 x15 x16 .
0
)
)
0
)
)
)
=
Inj1
(
x3
(
λ x9 :
(
ι →
ι → ι
)
→ ι
.
λ x10 x11 .
λ x12 :
ι → ι
.
setsum
0
(
x12
(
Inj0
0
)
)
)
0
)
)
⟶
(
∀ x4 .
∀ x5 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x6 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
.
∀ x7 .
x1
(
λ x9 :
ι →
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
Inj1
(
x1
(
λ x10 :
ι →
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
x2
(
λ x11 x12 :
(
ι → ι
)
→ ι
.
x0
(
λ x13 .
λ x14 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x13 .
0
)
(
λ x13 .
0
)
0
0
0
)
(
λ x11 .
λ x12 :
ι → ι
.
setsum
0
0
)
0
(
Inj1
0
)
)
(
λ x10 x11 x12 x13 .
x11
)
)
)
(
λ x9 x10 x11 x12 .
Inj1
x9
)
=
x7
)
⟶
(
∀ x4 :
ι →
ι → ι
.
∀ x5 .
∀ x6 :
ι → ι
.
∀ x7 .
x0
(
λ x9 .
λ x10 :
(
ι →
ι → ι
)
→ ι
.
x7
)
(
λ x9 .
x3
(
λ x10 :
(
ι →
ι → ι
)
→ ι
.
λ x11 x12 .
λ x13 :
ι → ι
.
Inj0
0
)
(
x3
(
λ x10 :
(
ι →
ι → ι
)
→ ι
.
λ x11 x12 .
λ x13 :
ι → ι
.
0
)
(
Inj1
(
setsum
0
0
)
)
)
)
(
λ x9 .
x1
(
λ x10 :
ι →
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x10 x11 x12 x13 .
Inj0
0
)
)
x5
(
Inj1
(
setsum
(
Inj0
(
x0
(
λ x9 .
λ x10 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x9 .
0
)
(
λ x9 .
0
)
0
0
0
)
)
(
x4
0
0
)
)
)
(
x6
(
x2
(
λ x9 x10 :
(
ι → ι
)
→ ι
.
x2
(
λ x11 x12 :
(
ι → ι
)
→ ι
.
setsum
0
0
)
(
λ x11 .
λ x12 :
ι → ι
.
x9
(
λ x13 .
0
)
)
(
x2
(
λ x11 x12 :
(
ι → ι
)
→ ι
.
0
)
(
λ x11 .
λ x12 :
ι → ι
.
0
)
0
0
)
(
x9
(
λ x11 .
0
)
)
)
(
λ x9 .
λ x10 :
ι → ι
.
x7
)
(
setsum
0
(
x1
(
λ x9 :
ι →
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x9 x10 x11 x12 .
0
)
)
)
(
Inj1
(
x0
(
λ x9 .
λ x10 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x9 .
0
)
(
λ x9 .
0
)
0
0
0
)
)
)
)
=
setsum
(
x6
(
x3
(
λ x9 :
(
ι →
ι → ι
)
→ ι
.
λ x10 x11 .
λ x12 :
ι → ι
.
x9
(
λ x13 x14 .
0
)
)
(
x0
(
λ x9 .
λ x10 :
(
ι →
ι → ι
)
→ ι
.
x7
)
(
λ x9 .
x1
(
λ x10 :
ι →
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x10 x11 x12 x13 .
0
)
)
(
λ x9 .
setsum
0
0
)
0
(
x2
(
λ x9 x10 :
(
ι → ι
)
→ ι
.
0
)
(
λ x9 .
λ x10 :
ι → ι
.
0
)
0
0
)
(
x3
(
λ x9 :
(
ι →
ι → ι
)
→ ι
.
λ x10 x11 .
λ x12 :
ι → ι
.
0
)
0
)
)
)
)
(
x4
(
x4
0
0
)
(
Inj1
x5
)
)
)
⟶
(
∀ x4 .
∀ x5 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x6 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→ ι
.
∀ x7 .
x0
(
λ x9 .
λ x10 :
(
ι →
ι → ι
)
→ ι
.
x1
(
λ x11 :
ι →
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
x7
)
(
λ x11 x12 x13 x14 .
x14
)
)
(
λ x9 .
setsum
(
setsum
(
Inj0
0
)
(
x6
(
λ x10 .
λ x11 :
ι → ι
.
0
)
(
Inj0
0
)
(
λ x10 .
setsum
0
0
)
)
)
(
x5
(
λ x10 x11 .
Inj0
(
x1
(
λ x12 :
ι →
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x12 x13 x14 x15 .
0
)
)
)
(
λ x10 .
x1
(
λ x11 :
ι →
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
x11
0
(
λ x12 .
0
)
(
λ x12 .
0
)
0
)
(
λ x11 x12 x13 x14 .
0
)
)
(
x6
(
λ x10 .
λ x11 :
ι → ι
.
x0
(
λ x12 .
λ x13 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x12 .
0
)
(
λ x12 .
0
)
0
0
0
)
(
setsum
0
0
)
(
λ x10 .
x0
(
λ x11 .
λ x12 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x11 .
0
)
(
λ x11 .
0
)
0
0
0
)
)
)
)
(
λ x9 .
x9
)
0
(
x6
(
λ x9 .
λ x10 :
ι → ι
.
setsum
(
setsum
(
setsum
0
0
)
(
x1
(
λ x11 :
ι →
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x11 x12 x13 x14 .
0
)
)
)
(
x3
(
λ x11 :
(
ι →
ι → ι
)
→ ι
.
λ x12 x13 .
λ x14 :
ι → ι
.
0
)
x9
)
)
0
(
λ x9 .
0
)
)
(
Inj1
x7
)
=
x1
(
λ x9 :
ι →
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
x1
(
λ x10 :
ι →
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x10 x11 x12 x13 .
x13
)
)
(
λ x9 x10 x11 x12 .
x10
)
)
⟶
False
(proof)
Theorem
eaa86..
:
∀ x0 :
(
ι →
ι →
ι → ι
)
→
(
ι →
ι →
(
ι → ι
)
→ ι
)
→ ι
.
∀ x1 :
(
(
(
ι →
ι →
ι → ι
)
→ ι
)
→
(
(
ι →
ι → ι
)
→ ι
)
→ ι
)
→
ι → ι
.
∀ x2 :
(
ι → ι
)
→
ι →
ι → ι
.
∀ x3 :
(
ι →
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
(
∀ x4 x5 x6 .
∀ x7 :
ι →
ι →
ι →
ι → ι
.
x3
(
λ x9 x10 .
λ x11 :
ι →
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
setsum
0
(
x3
(
λ x14 x15 .
λ x16 :
ι →
ι → ι
.
λ x17 :
ι → ι
.
λ x18 .
x18
)
(
setsum
(
x1
(
λ x14 :
(
ι →
ι →
ι → ι
)
→ ι
.
λ x15 :
(
ι →
ι → ι
)
→ ι
.
0
)
0
)
)
(
x2
(
λ x14 .
x14
)
(
x2
(
λ x14 .
0
)
0
0
)
(
x2
(
λ x14 .
0
)
0
0
)
)
)
)
(
λ x9 .
x5
)
(
x3
(
λ x9 x10 .
λ x11 :
ι →
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
x0
(
λ x14 x15 x16 .
Inj1
(
x2
(
λ x17 .
0
)
0
0
)
)
(
λ x14 x15 .
λ x16 :
ι → ι
.
0
)
)
(
λ x9 .
setsum
(
x1
(
λ x10 :
(
ι →
ι →
ι → ι
)
→ ι
.
λ x11 :
(
ι →
ι → ι
)
→ ι
.
x0
(
λ x12 x13 x14 .
0
)
(
λ x12 x13 .
λ x14 :
ι → ι
.
0
)
)
x5
)
(
x1
(
λ x10 :
(
ι →
ι →
ι → ι
)
→ ι
.
λ x11 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
Inj0
0
)
)
)
x5
)
=
x3
(
λ x9 x10 .
λ x11 :
ι →
ι → ι
.
λ x12 :
ι → ι
.
Inj1
)
(
λ x9 .
setsum
0
(
Inj0
x9
)
)
(
x3
(
λ x9 x10 .
λ x11 :
ι →
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
0
)
(
λ x9 .
0
)
x6
)
)
⟶
(
∀ x4 :
ι →
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
∀ x5 x6 x7 .
x3
(
λ x9 x10 .
λ x11 :
ι →
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
x11
(
Inj0
(
setsum
(
x0
(
λ x14 x15 x16 .
0
)
(
λ x14 x15 .
λ x16 :
ι → ι
.
0
)
)
0
)
)
(
setsum
0
(
x12
(
x2
(
λ x14 .
0
)
0
0
)
)
)
)
(
λ x9 .
x9
)
(
x4
(
Inj1
(
x2
(
λ x9 .
0
)
0
0
)
)
(
λ x9 :
ι → ι
.
x6
)
(
Inj1
x7
)
(
x1
(
λ x9 :
(
ι →
ι →
ι → ι
)
→ ι
.
λ x10 :
(
ι →
ι → ι
)
→ ι
.
x7
)
(
x4
x7
(
λ x9 :
ι → ι
.
x0
(
λ x10 x11 x12 .
0
)
(
λ x10 x11 .
λ x12 :
ι → ι
.
0
)
)
(
Inj1
0
)
(
setsum
0
0
)
)
)
)
=
x4
(
x1
(
λ x9 :
(
ι →
ι →
ι → ι
)
→ ι
.
λ x10 :
(
ι →
ι → ι
)
→ ι
.
Inj0
(
x1
(
λ x11 :
(
ι →
ι →
ι → ι
)
→ ι
.
λ x12 :
(
ι →
ι → ι
)
→ ι
.
x11
(
λ x13 x14 x15 .
0
)
)
(
Inj0
0
)
)
)
0
)
(
λ x9 :
ι → ι
.
Inj1
(
x0
(
λ x10 x11 x12 .
x2
(
λ x13 .
0
)
(
setsum
0
0
)
0
)
(
λ x10 x11 .
λ x12 :
ι → ι
.
x11
)
)
)
x6
(
setsum
(
x4
(
x0
(
λ x9 x10 x11 .
0
)
(
λ x9 x10 .
λ x11 :
ι → ι
.
0
)
)
(
λ x9 :
ι → ι
.
Inj0
x5
)
(
x1
(
λ x9 :
(
ι →
ι →
ι → ι
)
→ ι
.
λ x10 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
x3
(
λ x9 x10 .
λ x11 :
ι →
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
0
)
(
λ x9 .
0
)
0
)
)
(
x3
(
λ x9 x10 .
λ x11 :
ι →
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
setsum
0
0
)
(
λ x9 .
x5
)
0
)
)
0
)
)
⟶
(
∀ x4 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
∀ x5 :
ι → ι
.
∀ x6 x7 .
x2
(
λ x9 .
x9
)
(
Inj1
0
)
(
x1
(
λ x9 :
(
ι →
ι →
ι → ι
)
→ ι
.
λ x10 :
(
ι →
ι → ι
)
→ ι
.
x7
)
(
x2
(
λ x9 .
x6
)
(
x1
(
λ x9 :
(
ι →
ι →
ι → ι
)
→ ι
.
λ x10 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
setsum
0
0
)
)
(
x0
(
λ x9 x10 x11 .
x11
)
(
λ x9 x10 .
λ x11 :
ι → ι
.
x7
)
)
)
)
=
Inj0
(
x4
(
λ x9 .
λ x10 :
ι → ι
.
0
)
)
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 x7 .
x2
(
λ x9 .
x9
)
x4
(
Inj1
(
setsum
(
x5
x7
)
(
x0
(
λ x9 x10 x11 .
setsum
0
0
)
(
λ x9 x10 .
λ x11 :
ι → ι
.
0
)
)
)
)
=
x4
)
⟶
(
∀ x4 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x5 :
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x6 x7 .
x1
(
λ x9 :
(
ι →
ι →
ι → ι
)
→ ι
.
λ x10 :
(
ι →
ι → ι
)
→ ι
.
x3
(
λ x11 x12 .
λ x13 :
ι →
ι → ι
.
λ x14 :
ι → ι
.
λ x15 .
Inj0
0
)
(
λ x11 .
0
)
(
Inj1
(
Inj1
(
x1
(
λ x11 :
(
ι →
ι →
ι → ι
)
→ ι
.
λ x12 :
(
ι →
ι → ι
)
→ ι
.
0
)
0
)
)
)
)
0
=
x3
(
λ x9 x10 .
λ x11 :
ι →
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
Inj1
0
)
(
λ x9 .
setsum
(
x1
(
λ x10 :
(
ι →
ι →
ι → ι
)
→ ι
.
λ x11 :
(
ι →
ι → ι
)
→ ι
.
x0
(
λ x12 x13 x14 .
0
)
(
λ x12 x13 .
λ x14 :
ι → ι
.
setsum
0
0
)
)
(
setsum
(
x2
(
λ x10 .
0
)
0
0
)
x6
)
)
(
Inj0
(
setsum
0
x6
)
)
)
(
setsum
0
(
x3
(
λ x9 x10 .
λ x11 :
ι →
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
Inj1
(
x11
0
0
)
)
(
λ x9 .
x1
(
λ x10 :
(
ι →
ι →
ι → ι
)
→ ι
.
λ x11 :
(
ι →
ι → ι
)
→ ι
.
0
)
0
)
(
Inj0
(
x1
(
λ x9 :
(
ι →
ι →
ι → ι
)
→ ι
.
λ x10 :
(
ι →
ι → ι
)
→ ι
.
0
)
0
)
)
)
)
)
⟶
(
∀ x4 :
(
(
ι →
ι → ι
)
→ ι
)
→
ι →
ι →
ι → ι
.
∀ x5 :
(
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x6 .
∀ x7 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
x1
(
λ x9 :
(
ι →
ι →
ι → ι
)
→ ι
.
λ x10 :
(
ι →
ι → ι
)
→ ι
.
x9
(
λ x11 x12 x13 .
Inj1
(
x2
(
λ x14 .
0
)
(
Inj0
0
)
(
x2
(
λ x14 .
0
)
0
0
)
)
)
)
(
Inj0
(
x0
(
λ x9 x10 .
x3
(
λ x11 x12 .
λ x13 :
ι →
ι → ι
.
λ x14 :
ι → ι
.
λ x15 .
x3
(
λ x16 x17 .
λ x18 :
ι →
ι → ι
.
λ x19 :
ι → ι
.
λ x20 .
0
)
(
λ x16 .
0
)
0
)
(
λ x11 .
x10
)
)
(
λ x9 x10 .
λ x11 :
ι → ι
.
x9
)
)
)
=
setsum
(
x0
(
λ x9 x10 x11 .
0
)
(
λ x9 x10 .
λ x11 :
ι → ι
.
setsum
(
x0
(
λ x12 x13 x14 .
x1
(
λ x15 :
(
ι →
ι →
ι → ι
)
→ ι
.
λ x16 :
(
ι →
ι → ι
)
→ ι
.
0
)
0
)
(
λ x12 x13 .
λ x14 :
ι → ι
.
0
)
)
0
)
)
0
)
⟶
(
∀ x4 .
∀ x5 :
(
ι →
ι → ι
)
→ ι
.
∀ x6 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι → ι
.
∀ x7 .
x0
(
λ x9 x10 x11 .
0
)
(
λ x9 x10 .
λ x11 :
ι → ι
.
x10
)
=
x6
(
λ x9 :
(
ι → ι
)
→ ι
.
setsum
(
x5
(
λ x10 x11 .
x11
)
)
0
)
x4
)
⟶
(
∀ x4 .
∀ x5 :
(
(
ι →
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x6 x7 .
x0
(
λ x9 x10 x11 .
x7
)
(
λ x9 x10 .
λ x11 :
ι → ι
.
Inj0
(
x0
(
λ x12 x13 x14 .
setsum
0
(
Inj0
0
)
)
(
λ x12 x13 .
λ x14 :
ι → ι
.
x13
)
)
)
=
x7
)
⟶
False
(proof)
Theorem
bbce6..
:
∀ x0 :
(
ι →
(
(
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
∀ x1 :
(
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
ι → ι
.
∀ x2 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι → ι
.
∀ x3 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
(
∀ x4 x5 x6 x7 .
x3
(
λ x9 :
ι → ι
.
λ x10 .
x6
)
(
x0
(
λ x9 .
λ x10 :
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x11 x12 :
ι → ι
.
λ x13 .
Inj0
(
x10
(
λ x14 .
Inj0
0
)
(
λ x14 .
0
)
)
)
)
=
setsum
(
setsum
0
(
x1
(
λ x9 :
ι →
(
ι → ι
)
→ ι
.
λ x10 .
setsum
(
x3
(
λ x11 :
ι → ι
.
λ x12 .
0
)
(
λ x11 .
0
)
)
x7
)
(
x3
(
λ x9 :
ι → ι
.
λ x10 .
x3
(
λ x11 :
ι → ι
.
λ x12 .
0
)
(
λ x11 .
0
)
)
(
λ x9 .
x1
(
λ x10 :
ι →
(
ι → ι
)
→ ι
.
λ x11 .
0
)
0
)
)
)
)
(
Inj0
x4
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
ι → ι
.
∀ x7 .
x3
(
λ x9 :
ι → ι
.
λ x10 .
0
)
(
λ x9 .
setsum
0
(
x3
(
λ x10 :
ι → ι
.
λ x11 .
x2
(
λ x12 :
(
ι → ι
)
→ ι
.
x2
(
λ x13 :
(
ι → ι
)
→ ι
.
0
)
0
)
x9
)
(
λ x10 .
x1
(
λ x11 :
ι →
(
ι → ι
)
→ ι
.
λ x12 .
Inj1
0
)
x7
)
)
)
=
x5
)
⟶
(
∀ x4 .
∀ x5 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
∀ x6 :
ι →
ι →
ι → ι
.
∀ x7 .
x2
(
λ x9 :
(
ι → ι
)
→ ι
.
x5
(
λ x10 .
λ x11 :
ι → ι
.
x9
(
λ x12 .
0
)
)
(
x2
(
λ x10 :
(
ι → ι
)
→ ι
.
x7
)
0
)
(
λ x10 .
0
)
(
Inj0
x7
)
)
(
Inj1
(
x6
x4
(
x6
(
x1
(
λ x9 :
ι →
(
ι → ι
)
→ ι
.
λ x10 .
0
)
0
)
(
x0
(
λ x9 .
λ x10 :
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x11 x12 :
ι → ι
.
λ x13 .
0
)
0
)
(
x1
(
λ x9 :
ι →
(
ι → ι
)
→ ι
.
λ x10 .
0
)
0
)
)
0
)
)
=
Inj1
(
x5
(
λ x9 .
λ x10 :
ι → ι
.
x7
)
(
Inj1
(
Inj0
(
setsum
0
0
)
)
)
(
λ x9 .
0
)
0
)
)
⟶
(
∀ x4 :
ι →
(
ι →
ι → ι
)
→
ι → ι
.
∀ x5 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x6 .
∀ x7 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
x2
(
λ x9 :
(
ι → ι
)
→ ι
.
x3
(
λ x10 :
ι → ι
.
x10
)
(
λ x10 .
x7
(
setsum
(
x1
(
λ x11 :
ι →
(
ι → ι
)
→ ι
.
λ x12 .
0
)
0
)
0
)
0
(
λ x11 .
Inj0
(
x2
(
λ x12 :
(
ι → ι
)
→ ι
.
0
)
0
)
)
(
x3
(
λ x11 :
ι → ι
.
λ x12 .
Inj0
0
)
(
λ x11 .
0
)
)
)
)
(
setsum
0
0
)
=
x3
(
λ x9 :
ι → ι
.
λ x10 .
setsum
(
x2
(
λ x11 :
(
ι → ι
)
→ ι
.
setsum
(
x0
(
λ x12 .
λ x13 :
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x14 x15 :
ι → ι
.
λ x16 .
0
)
0
)
(
x2
(
λ x12 :
(
ι → ι
)
→ ι
.
0
)
0
)
)
(
setsum
(
x0
(
λ x11 .
λ x12 :
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x13 x14 :
ι → ι
.
λ x15 .
0
)
0
)
(
x1
(
λ x11 :
ι →
(
ι → ι
)
→ ι
.
λ x12 .
0
)
0
)
)
)
(
x0
(
λ x11 .
λ x12 :
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x13 x14 :
ι → ι
.
λ x15 .
0
)
(
setsum
(
setsum
0
0
)
(
x2
(
λ x11 :
(
ι → ι
)
→ ι
.
0
)
0
)
)
)
)
(
λ x9 .
Inj0
(
Inj1
0
)
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→ ι
.
∀ x5 :
(
(
ι →
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
∀ x6 x7 .
x1
(
λ x9 :
ι →
(
ι → ι
)
→ ι
.
λ x10 .
Inj0
(
x2
(
λ x11 :
(
ι → ι
)
→ ι
.
0
)
(
Inj0
0
)
)
)
(
setsum
(
x0
(
λ x9 .
λ x10 :
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x11 x12 :
ι → ι
.
λ x13 .
Inj1
0
)
0
)
(
Inj0
0
)
)
=
x5
(
λ x9 :
ι →
ι → ι
.
0
)
(
λ x9 x10 .
0
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 x6 x7 .
x1
(
λ x9 :
ι →
(
ι → ι
)
→ ι
.
λ x10 .
x3
(
λ x11 :
ι → ι
.
λ x12 .
x2
(
λ x13 :
(
ι → ι
)
→ ι
.
setsum
0
(
x2
(
λ x14 :
(
ι → ι
)
→ ι
.
0
)
0
)
)
(
x2
(
λ x13 :
(
ι → ι
)
→ ι
.
0
)
x10
)
)
(
λ x11 .
setsum
(
Inj1
0
)
(
x0
(
λ x12 .
λ x13 :
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x14 x15 :
ι → ι
.
λ x16 .
x13
(
λ x17 .
0
)
(
λ x17 .
0
)
)
(
x9
0
(
λ x12 .
0
)
)
)
)
)
(
x0
(
λ x9 .
λ x10 :
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x11 x12 :
ι → ι
.
λ x13 .
x2
(
λ x14 :
(
ι → ι
)
→ ι
.
Inj0
(
Inj0
0
)
)
(
Inj1
(
setsum
0
0
)
)
)
(
x4
(
Inj1
0
)
)
)
=
x0
(
λ x9 .
λ x10 :
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x11 x12 :
ι → ι
.
λ x13 .
x12
(
x10
(
λ x14 .
x14
)
(
λ x14 .
0
)
)
)
(
Inj0
(
setsum
(
Inj0
(
x3
(
λ x9 :
ι → ι
.
λ x10 .
0
)
(
λ x9 .
0
)
)
)
(
x0
(
λ x9 .
λ x10 :
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x11 x12 :
ι → ι
.
λ x13 .
x2
(
λ x14 :
(
ι → ι
)
→ ι
.
0
)
0
)
(
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 :
(
(
ι →
ι → ι
)
→ ι
)
→
ι → ι
.
∀ x5 :
ι →
(
ι → ι
)
→
ι →
ι → ι
.
∀ x6 .
∀ x7 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
.
x0
(
λ x9 .
λ x10 :
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x11 x12 :
ι → ι
.
λ x13 .
x11
(
setsum
x13
(
x3
(
λ x14 :
ι → ι
.
λ x15 .
x3
(
λ x16 :
ι → ι
.
λ x17 .
0
)
(
λ x16 .
0
)
)
(
λ x14 .
x12
0
)
)
)
)
(
x4
(
λ x9 :
ι →
ι → ι
.
0
)
(
setsum
0
0
)
)
=
setsum
0
(
setsum
(
x0
(
λ x9 .
λ x10 :
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x11 x12 :
ι → ι
.
λ x13 .
0
)
0
)
0
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x5 x6 .
∀ x7 :
ι → ι
.
x0
(
λ x9 .
λ x10 :
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x11 x12 :
ι → ι
.
λ x13 .
0
)
(
x3
(
λ x9 :
ι → ι
.
λ x10 .
0
)
(
λ x9 .
0
)
)
=
setsum
(
x1
(
λ x9 :
ι →
(
ι → ι
)
→ ι
.
λ x10 .
0
)
0
)
0
)
⟶
False
(proof)
Theorem
d61cb..
:
∀ x0 :
(
(
ι →
(
ι →
ι → ι
)
→ ι
)
→ ι
)
→
(
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→ ι
)
→
ι → ι
.
∀ x1 :
(
(
(
ι →
ι →
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→
(
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
ι → ι
)
→ ι
.
∀ x2 :
(
ι →
ι →
ι →
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
∀ x3 :
(
(
(
(
(
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
.
(
∀ x4 x5 x6 x7 .
x3
(
λ x9 :
(
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→ ι
.
λ x10 :
ι →
ι →
ι → ι
.
λ x11 :
(
ι → ι
)
→
ι → ι
.
setsum
(
x9
(
λ x12 :
(
ι → ι
)
→
ι → ι
.
λ x13 .
x2
(
λ x14 x15 x16 .
λ x17 :
ι → ι
.
λ x18 .
0
)
(
setsum
0
0
)
)
)
(
setsum
(
Inj0
0
)
(
x0
(
λ x12 :
ι →
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x12 :
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
0
)
0
)
)
)
(
x1
(
λ x9 :
(
ι →
ι →
ι → ι
)
→
ι → ι
.
λ x10 .
Inj0
(
x3
(
λ x11 :
(
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→ ι
.
λ x12 :
ι →
ι →
ι → ι
.
λ x13 :
(
ι → ι
)
→
ι → ι
.
x2
(
λ x14 x15 x16 .
λ x17 :
ι → ι
.
λ x18 .
0
)
0
)
x10
(
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 :
ι → ι
.
x3
(
λ x13 :
(
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→ ι
.
λ x14 :
ι →
ι →
ι → ι
.
λ x15 :
(
ι → ι
)
→
ι → ι
.
0
)
0
(
λ x13 :
(
ι → ι
)
→
ι → ι
.
λ x14 :
ι → ι
.
0
)
(
λ x13 :
ι → ι
.
0
)
0
)
(
λ x11 :
ι → ι
.
Inj1
0
)
x10
)
)
(
λ x9 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x10 .
x0
(
λ x11 :
ι →
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x11 :
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
0
)
(
setsum
(
Inj1
0
)
(
setsum
0
0
)
)
)
)
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 :
ι → ι
.
x2
(
λ x11 x12 x13 .
λ x14 :
ι → ι
.
λ x15 .
x12
)
(
x10
0
)
)
(
λ x9 :
ι → ι
.
x7
)
0
=
x1
(
λ x9 :
(
ι →
ι →
ι → ι
)
→
ι → ι
.
λ x10 .
Inj0
(
x3
(
λ x11 :
(
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→ ι
.
λ x12 :
ι →
ι →
ι → ι
.
λ x13 :
(
ι → ι
)
→
ι → ι
.
0
)
0
(
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 :
ι → ι
.
Inj1
(
x3
(
λ x13 :
(
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→ ι
.
λ x14 :
ι →
ι →
ι → ι
.
λ x15 :
(
ι → ι
)
→
ι → ι
.
0
)
0
(
λ x13 :
(
ι → ι
)
→
ι → ι
.
λ x14 :
ι → ι
.
0
)
(
λ x13 :
ι → ι
.
0
)
0
)
)
(
λ x11 :
ι → ι
.
x1
(
λ x12 :
(
ι →
ι →
ι → ι
)
→
ι → ι
.
λ x13 .
x10
)
(
λ x12 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x13 .
x13
)
)
(
x9
(
λ x11 x12 x13 .
x1
(
λ x14 :
(
ι →
ι →
ι → ι
)
→
ι → ι
.
λ x15 .
0
)
(
λ x14 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x15 .
0
)
)
0
)
)
)
(
λ x9 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x10 .
x1
(
λ x11 :
(
ι →
ι →
ι → ι
)
→
ι → ι
.
λ x12 .
x10
)
(
λ x11 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x12 .
x11
(
λ x13 x14 .
x3
(
λ x15 :
(
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→ ι
.
λ x16 :
ι →
ι →
ι → ι
.
λ x17 :
(
ι → ι
)
→
ι → ι
.
0
)
0
(
λ x15 :
(
ι → ι
)
→
ι → ι
.
λ x16 :
ι → ι
.
0
)
(
λ x15 :
ι → ι
.
setsum
0
0
)
(
Inj1
0
)
)
(
λ x13 .
0
)
)
)
)
⟶
(
∀ x4 x5 x6 x7 .
x3
(
λ x9 :
(
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→ ι
.
λ x10 :
ι →
ι →
ι → ι
.
λ x11 :
(
ι → ι
)
→
ι → ι
.
0
)
0
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 :
ι → ι
.
Inj1
(
x0
(
λ x11 :
ι →
(
ι →
ι → ι
)
→ ι
.
x0
(
λ x12 :
ι →
(
ι →
ι → ι
)
→ ι
.
x2
(
λ x13 x14 x15 .
λ x16 :
ι → ι
.
λ x17 .
0
)
0
)
(
λ x12 :
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
x10
0
)
0
)
(
λ x11 :
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
0
)
0
)
)
(
λ x9 :
ι → ι
.
0
)
(
Inj0
0
)
=
x4
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 .
∀ x7 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι →
ι →
ι → ι
.
x2
(
λ x9 x10 x11 .
λ x12 :
ι → ι
.
λ x13 .
setsum
0
(
setsum
(
setsum
0
(
setsum
0
0
)
)
x10
)
)
0
=
x5
x6
)
⟶
(
∀ x4 .
∀ x5 :
ι →
ι →
(
ι → ι
)
→ ι
.
∀ x6 .
∀ x7 :
(
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
x2
(
λ x9 x10 x11 .
λ x12 :
ι → ι
.
λ x13 .
x2
(
λ x14 x15 x16 .
λ x17 :
ι → ι
.
λ x18 .
x16
)
0
)
(
x2
(
λ x9 x10 x11 .
λ x12 :
ι → ι
.
λ x13 .
0
)
0
)
=
x2
(
λ x9 x10 x11 .
λ x12 :
ι → ι
.
λ x13 .
Inj1
(
x2
(
λ x14 x15 x16 .
λ x17 :
ι → ι
.
λ x18 .
setsum
(
x3
(
λ x19 :
(
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→ ι
.
λ x20 :
ι →
ι →
ι → ι
.
λ x21 :
(
ι → ι
)
→
ι → ι
.
0
)
0
(
λ x19 :
(
ι → ι
)
→
ι → ι
.
λ x20 :
ι → ι
.
0
)
(
λ x19 :
ι → ι
.
0
)
0
)
(
x1
(
λ x19 :
(
ι →
ι →
ι → ι
)
→
ι → ι
.
λ x20 .
0
)
(
λ x19 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x20 .
0
)
)
)
(
x12
(
Inj0
0
)
)
)
)
x6
)
⟶
(
∀ x4 x5 x6 x7 .
x1
(
λ x9 :
(
ι →
ι →
ι → ι
)
→
ι → ι
.
λ x10 .
x2
(
λ x11 x12 x13 .
λ x14 :
ι → ι
.
λ x15 .
x15
)
(
Inj1
(
x2
(
λ x11 x12 x13 .
λ x14 :
ι → ι
.
λ x15 .
0
)
(
x9
(
λ x11 x12 x13 .
0
)
0
)
)
)
)
(
λ x9 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x10 .
0
)
=
setsum
(
x0
(
λ x9 :
ι →
(
ι →
ι → ι
)
→ ι
.
x5
)
(
λ x9 :
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
Inj1
x7
)
(
Inj1
(
x1
(
λ x9 :
(
ι →
ι →
ι → ι
)
→
ι → ι
.
λ x10 .
x9
(
λ x11 x12 x13 .
0
)
0
)
(
λ x9 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x10 .
x6
)
)
)
)
0
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 x6 .
∀ x7 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
x1
(
λ x9 :
(
ι →
ι →
ι → ι
)
→
ι → ι
.
λ x10 .
Inj0
(
x1
(
λ x11 :
(
ι →
ι →
ι → ι
)
→
ι → ι
.
λ x12 .
Inj1
(
Inj1
0
)
)
(
λ x11 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x12 .
0
)
)
)
(
λ x9 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x10 .
0
)
=
x4
(
setsum
(
Inj0
0
)
(
Inj1
0
)
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→ ι
.
∀ x5 x6 .
∀ x7 :
(
ι →
ι →
ι → ι
)
→ ι
.
x0
(
λ x9 :
ι →
(
ι →
ι → ι
)
→ ι
.
setsum
(
setsum
0
(
x7
(
λ x10 x11 x12 .
x11
)
)
)
(
x9
0
(
λ x10 x11 .
Inj0
(
Inj0
0
)
)
)
)
(
λ x9 :
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
setsum
x6
0
)
x6
=
x6
)
⟶
(
∀ x4 x5 .
∀ x6 :
(
ι →
ι → ι
)
→
ι →
ι → ι
.
∀ x7 .
x0
(
λ x9 :
ι →
(
ι →
ι → ι
)
→ ι
.
x1
(
λ x10 :
(
ι →
ι →
ι → ι
)
→
ι → ι
.
λ x11 .
x9
0
(
λ x12 x13 .
0
)
)
(
λ x10 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x11 .
0
)
)
(
λ x9 :
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
Inj1
(
Inj0
x7
)
)
(
setsum
(
x3
(
λ x9 :
(
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→ ι
.
λ x10 :
ι →
ι →
ι → ι
.
λ x11 :
(
ι → ι
)
→
ι → ι
.
x1
(
λ x12 :
(
ι →
ι →
ι → ι
)
→
ι → ι
.
λ x13 .
x2
(
λ x14 x15 x16 .
λ x17 :
ι → ι
.
λ x18 .
0
)
0
)
(
λ x12 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x13 .
x11
(
λ x14 .
0
)
0
)
)
(
x1
(
λ x9 :
(
ι →
ι →
ι → ι
)
→
ι → ι
.
λ x10 .
x9
(
λ x11 x12 x13 .
0
)
0
)
(
λ x9 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x10 .
0
)
)
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 :
ι → ι
.
x1
(
λ x11 :
(
ι →
ι →
ι → ι
)
→
ι → ι
.
λ x12 .
setsum
0
0
)
(
λ x11 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x12 .
Inj0
0
)
)
(
λ x9 :
ι → ι
.
Inj1
(
setsum
0
0
)
)
0
)
(
Inj1
x4
)
)
=
x1
(
λ x9 :
(
ι →
ι →
ι → ι
)
→
ι → ι
.
λ x10 .
x6
(
λ x11 .
setsum
(
x3
(
λ x12 :
(
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→ ι
.
λ x13 :
ι →
ι →
ι → ι
.
λ x14 :
(
ι → ι
)
→
ι → ι
.
x14
(
λ x15 .
0
)
0
)
(
x1
(
λ x12 :
(
ι →
ι →
ι → ι
)
→
ι → ι
.
λ x13 .
0
)
(
λ x12 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x13 .
0
)
)
(
λ x12 :
(
ι → ι
)
→
ι → ι
.
λ x13 :
ι → ι
.
0
)
(
λ x12 :
ι → ι
.
setsum
0
0
)
(
x2
(
λ x12 x13 x14 .
λ x15 :
ι → ι
.
λ x16 .
0
)
0
)
)
)
0
(
x0
(
λ x11 :
ι →
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x11 :
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
x11
(
λ x12 :
ι → ι
.
0
)
(
setsum
0
0
)
(
Inj1
0
)
)
(
setsum
(
Inj1
0
)
(
x2
(
λ x11 x12 x13 .
λ x14 :
ι → ι
.
λ x15 .
0
)
0
)
)
)
)
(
λ x9 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x10 .
Inj0
(
setsum
(
Inj1
0
)
(
x2
(
λ x11 x12 x13 .
λ x14 :
ι → ι
.
λ x15 .
Inj0
0
)
0
)
)
)
)
⟶
False
(proof)
Theorem
594e6..
:
∀ 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
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x1 :
(
(
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
)
→
ι →
ι →
(
ι → ι
)
→ ι
)
→
ι →
ι →
ι →
(
ι → ι
)
→
ι → ι
.
∀ x2 :
(
ι → ι
)
→
ι → ι
.
∀ x3 :
(
ι →
ι → ι
)
→
(
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→ ι
)
→ ι
.
(
∀ x4 :
(
ι → ι
)
→ ι
.
∀ x5 :
ι →
(
ι →
ι → ι
)
→ ι
.
∀ x6 .
∀ x7 :
ι → ι
.
x3
(
λ x9 x10 .
0
)
(
λ x9 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
x3
(
λ x10 x11 .
setsum
0
(
x7
0
)
)
(
λ x10 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
x10
(
λ x11 :
ι → ι
.
setsum
(
setsum
0
0
)
(
x7
0
)
)
(
Inj1
(
setsum
0
0
)
)
)
)
=
x3
(
λ x9 x10 .
Inj0
(
setsum
x6
(
setsum
0
x10
)
)
)
(
λ x9 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
setsum
0
(
x0
(
λ x10 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
λ x11 :
ι →
ι →
ι → ι
.
λ x12 :
ι → ι
.
x12
0
)
(
λ x10 :
ι → ι
.
λ x11 .
λ x12 :
ι → ι
.
x2
(
λ x13 .
x0
(
λ x14 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
λ x15 :
ι →
ι →
ι → ι
.
λ x16 :
ι → ι
.
0
)
(
λ x14 :
ι → ι
.
λ x15 .
λ x16 :
ι → ι
.
0
)
(
λ x14 .
0
)
(
λ x14 :
ι → ι
.
λ x15 .
0
)
(
λ x14 .
0
)
)
(
Inj1
0
)
)
(
λ x10 .
Inj1
(
x1
(
λ x11 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
λ x12 x13 .
λ x14 :
ι → ι
.
0
)
0
0
0
(
λ x11 .
0
)
0
)
)
(
λ x10 :
ι → ι
.
λ x11 .
Inj0
(
x7
0
)
)
(
λ x10 .
x7
0
)
)
)
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
ι →
(
ι → ι
)
→
ι → ι
.
x3
(
λ x9 x10 .
setsum
(
x0
(
λ x11 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
λ x12 :
ι →
ι →
ι → ι
.
λ x13 :
ι → ι
.
0
)
(
λ x11 :
ι → ι
.
λ x12 .
λ x13 :
ι → ι
.
setsum
0
0
)
(
λ x11 .
0
)
(
λ x11 :
ι → ι
.
λ x12 .
0
)
(
λ x11 .
x11
)
)
x9
)
(
λ x9 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
setsum
(
x9
(
λ x10 :
ι → ι
.
x2
(
λ x11 .
Inj0
0
)
(
x3
(
λ x11 x12 .
0
)
(
λ x11 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
0
)
)
)
(
x2
(
λ x10 .
x0
(
λ x11 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
λ x12 :
ι →
ι →
ι → ι
.
λ x13 :
ι → ι
.
0
)
(
λ x11 :
ι → ι
.
λ x12 .
λ x13 :
ι → ι
.
0
)
(
λ x11 .
0
)
(
λ x11 :
ι → ι
.
λ x12 .
0
)
(
λ x11 .
0
)
)
(
Inj0
0
)
)
)
0
)
=
x6
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 :
ι →
(
ι → ι
)
→
ι →
ι → ι
.
∀ x6 :
ι →
ι → ι
.
∀ x7 .
x2
(
λ x9 .
x2
(
λ x10 .
x7
)
0
)
(
x0
(
λ x9 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
λ x10 :
ι →
ι →
ι → ι
.
λ x11 :
ι → ι
.
setsum
(
x9
(
λ x12 x13 x14 .
0
)
(
λ x12 :
ι → ι
.
x3
(
λ x13 x14 .
0
)
(
λ x13 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
0
)
)
(
x2
(
λ x12 .
0
)
0
)
)
(
x1
(
λ x12 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
λ x13 x14 .
λ x15 :
ι → ι
.
setsum
0
0
)
0
0
(
setsum
0
0
)
(
λ x12 .
x12
)
0
)
)
(
λ x9 :
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
x2
(
λ x12 .
0
)
(
Inj0
0
)
)
(
λ x9 .
0
)
(
λ x9 :
ι → ι
.
x1
(
λ x10 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
λ x11 x12 .
λ x13 :
ι → ι
.
0
)
x7
(
x9
0
)
0
(
λ x10 .
0
)
)
(
λ x9 .
setsum
(
x3
(
λ x10 x11 .
x9
)
(
λ x10 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
setsum
0
0
)
)
(
Inj0
0
)
)
)
=
Inj1
(
x4
(
x5
(
x1
(
λ x9 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
λ x10 x11 .
λ x12 :
ι → ι
.
x1
(
λ x13 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
λ x14 x15 .
λ x16 :
ι → ι
.
0
)
0
0
0
(
λ x13 .
0
)
0
)
(
setsum
0
0
)
0
(
Inj1
0
)
(
λ x9 .
x6
0
0
)
0
)
(
λ x9 .
x9
)
0
(
x4
(
x4
0
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 .
∀ x7 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
x2
(
λ x9 .
x1
(
λ x10 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
λ x11 x12 .
λ x13 :
ι → ι
.
x1
(
λ x14 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
λ x15 x16 .
λ x17 :
ι → ι
.
x3
(
λ x18 x19 .
x17
0
)
(
λ x18 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
x0
(
λ x19 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
λ x20 :
ι →
ι →
ι → ι
.
λ x21 :
ι → ι
.
0
)
(
λ x19 :
ι → ι
.
λ x20 .
λ x21 :
ι → ι
.
0
)
(
λ x19 .
0
)
(
λ x19 :
ι → ι
.
λ x20 .
0
)
(
λ x19 .
0
)
)
)
(
setsum
(
x10
(
λ x14 .
0
)
(
λ x14 x15 .
0
)
)
(
Inj1
0
)
)
(
setsum
(
x1
(
λ x14 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
λ x15 x16 .
λ x17 :
ι → ι
.
0
)
0
0
0
(
λ x14 .
0
)
0
)
(
x3
(
λ x14 x15 .
0
)
(
λ x14 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
0
)
)
)
x12
(
λ x14 .
setsum
x11
0
)
(
x1
(
λ x14 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
λ x15 x16 .
λ x17 :
ι → ι
.
Inj1
0
)
x11
(
setsum
0
0
)
(
setsum
0
0
)
(
λ x14 .
0
)
x11
)
)
(
x5
(
Inj1
0
)
)
(
setsum
0
(
x3
(
λ x10 x11 .
x9
)
(
λ x10 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
0
)
)
)
0
(
λ x10 .
0
)
(
x3
(
λ x10 x11 .
x9
)
(
λ x10 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
0
)
)
)
(
x3
(
λ x9 x10 .
x6
)
(
λ x9 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
x2
(
λ x10 .
x10
)
(
setsum
(
x7
(
λ x10 :
ι →
ι → ι
.
λ x11 :
ι → ι
.
λ x12 .
0
)
0
)
0
)
)
)
=
x1
(
λ x9 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
λ x10 x11 .
λ x12 :
ι → ι
.
Inj0
0
)
x6
(
x5
(
x0
(
λ x9 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
λ x10 :
ι →
ι →
ι → ι
.
λ x11 :
ι → ι
.
x3
(
λ x12 x13 .
x0
(
λ x14 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
λ x15 :
ι →
ι →
ι → ι
.
λ x16 :
ι → ι
.
0
)
(
λ x14 :
ι → ι
.
λ x15 .
λ x16 :
ι → ι
.
0
)
(
λ x14 .
0
)
(
λ x14 :
ι → ι
.
λ x15 .
0
)
(
λ x14 .
0
)
)
(
λ x12 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
0
)
)
(
λ x9 :
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
setsum
(
setsum
0
0
)
(
x3
(
λ x12 x13 .
0
)
(
λ x12 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
0
)
)
)
(
λ x9 .
setsum
0
0
)
(
λ x9 :
ι → ι
.
λ x10 .
x2
(
λ x11 .
Inj1
0
)
(
setsum
0
0
)
)
(
λ x9 .
Inj1
(
setsum
0
0
)
)
)
)
(
setsum
(
Inj1
(
x1
(
λ x9 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
λ x10 x11 .
λ x12 :
ι → ι
.
x10
)
0
0
(
x0
(
λ x9 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
λ x10 :
ι →
ι →
ι → ι
.
λ x11 :
ι → ι
.
0
)
(
λ x9 :
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
0
)
(
λ x9 .
0
)
(
λ x9 :
ι → ι
.
λ x10 .
0
)
(
λ x9 .
0
)
)
(
λ x9 .
x9
)
(
x3
(
λ x9 x10 .
0
)
(
λ x9 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
0
)
)
)
)
0
)
(
λ x9 .
Inj1
0
)
(
x7
(
λ x9 :
ι →
ι → ι
.
λ x10 :
ι → ι
.
λ x11 .
x7
(
λ x12 :
ι →
ι → ι
.
λ x13 :
ι → ι
.
setsum
x11
)
(
x9
(
Inj1
0
)
(
x1
(
λ x12 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
λ x13 x14 .
λ x15 :
ι → ι
.
0
)
0
0
0
(
λ x12 .
0
)
0
)
)
)
0
)
)
⟶
(
∀ x4 :
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x5 .
∀ x6 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
∀ x7 .
x1
(
λ x9 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
λ x10 x11 .
λ x12 :
ι → ι
.
x9
(
λ x13 .
x10
)
(
λ x13 x14 .
x11
)
)
(
x3
(
λ x9 x10 .
x2
(
λ x11 .
0
)
(
x3
(
λ x11 x12 .
x0
(
λ x13 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
λ x14 :
ι →
ι →
ι → ι
.
λ x15 :
ι → ι
.
0
)
(
λ x13 :
ι → ι
.
λ x14 .
λ x15 :
ι → ι
.
0
)
(
λ x13 .
0
)
(
λ x13 :
ι → ι
.
λ x14 .
0
)
(
λ x13 .
0
)
)
(
λ x11 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
x3
(
λ x12 x13 .
0
)
(
λ x12 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
0
)
)
)
)
(
λ x9 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
x6
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 :
ι → ι
.
x7
)
)
)
(
x3
(
λ x9 x10 .
x3
(
λ x11 x12 .
x11
)
(
λ x11 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
x1
(
λ x12 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
λ x13 x14 .
λ x15 :
ι → ι
.
Inj1
0
)
(
x0
(
λ x12 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
λ x13 :
ι →
ι →
ι → ι
.
λ x14 :
ι → ι
.
0
)
(
λ x12 :
ι → ι
.
λ x13 .
λ x14 :
ι → ι
.
0
)
(
λ x12 .
0
)
(
λ x12 :
ι → ι
.
λ x13 .
0
)
(
λ x12 .
0
)
)
(
x1
(
λ x12 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
λ x13 x14 .
λ x15 :
ι → ι
.
0
)
0
0
0
(
λ x12 .
0
)
0
)
(
x2
(
λ x12 .
0
)
0
)
(
λ x12 .
Inj0
0
)
0
)
)
(
λ x9 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
x6
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 :
ι → ι
.
Inj1
(
Inj1
0
)
)
)
)
x7
(
λ x9 .
x6
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 :
ι → ι
.
0
)
)
(
x2
(
λ x9 .
0
)
x7
)
=
setsum
(
x3
(
λ x9 x10 .
x1
(
λ x11 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
λ x12 x13 .
λ x14 :
ι → ι
.
setsum
0
(
setsum
0
0
)
)
0
(
setsum
x10
0
)
x9
(
λ x11 .
x11
)
(
setsum
(
Inj0
0
)
0
)
)
(
λ x9 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
setsum
0
(
Inj0
0
)
)
)
(
Inj1
(
Inj0
(
x6
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 :
ι → ι
.
0
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 x7 .
x1
(
λ x9 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
λ x10 x11 .
λ x12 :
ι → ι
.
x2
(
λ x13 .
setsum
x10
x10
)
(
x0
(
λ x13 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
λ x14 :
ι →
ι →
ι → ι
.
λ x15 :
ι → ι
.
x15
(
x3
(
λ x16 x17 .
0
)
(
λ x16 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
0
)
)
)
(
λ x13 :
ι → ι
.
λ x14 .
λ x15 :
ι → ι
.
x1
(
λ x16 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
λ x17 x18 .
λ x19 :
ι → ι
.
x18
)
(
x1
(
λ x16 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
λ x17 x18 .
λ x19 :
ι → ι
.
0
)
0
0
0
(
λ x16 .
0
)
0
)
(
Inj0
0
)
(
x12
0
)
(
λ x16 .
0
)
0
)
(
λ x13 .
setsum
(
x2
(
λ x14 .
0
)
0
)
0
)
(
λ x13 :
ι → ι
.
λ x14 .
x14
)
(
λ x13 .
Inj1
x10
)
)
)
(
x5
(
x3
(
λ x9 x10 .
x2
(
λ x11 .
0
)
0
)
(
λ x9 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
x2
(
λ x10 .
setsum
0
0
)
(
x2
(
λ x10 .
0
)
0
)
)
)
)
(
Inj0
(
x1
(
λ x9 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
λ x10 x11 .
λ x12 :
ι → ι
.
x1
(
λ x13 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
λ x14 x15 .
λ x16 :
ι → ι
.
Inj0
0
)
0
(
x0
(
λ x13 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
λ x14 :
ι →
ι →
ι → ι
.
λ x15 :
ι → ι
.
0
)
(
λ x13 :
ι → ι
.
λ x14 .
λ x15 :
ι → ι
.
0
)
(
λ x13 .
0
)
(
λ x13 :
ι → ι
.
λ x14 .
0
)
(
λ x13 .
0
)
)
(
setsum
0
0
)
(
λ x13 .
0
)
0
)
(
Inj1
(
setsum
0
0
)
)
(
x0
(
λ x9 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
λ x10 :
ι →
ι →
ι → ι
.
λ x11 :
ι → ι
.
x2
(
λ x12 .
0
)
0
)
(
λ x9 :
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
0
)
(
λ x9 .
Inj0
0
)
(
λ x9 :
ι → ι
.
λ x10 .
x6
)
(
λ x9 .
Inj0
0
)
)
(
Inj1
(
Inj1
0
)
)
(
λ x9 .
x7
)
(
Inj0
0
)
)
)
(
x0
(
λ x9 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
λ x10 :
ι →
ι →
ι → ι
.
λ x11 :
ι → ι
.
x9
(
λ x12 x13 x14 .
0
)
(
λ x12 :
ι → ι
.
Inj1
0
)
(
x3
(
λ x12 x13 .
x10
0
0
0
)
(
λ x12 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
0
)
)
)
(
λ x9 :
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
x3
(
λ x12 x13 .
x2
(
λ x14 .
x0
(
λ x15 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
λ x16 :
ι →
ι →
ι → ι
.
λ x17 :
ι → ι
.
0
)
(
λ x15 :
ι → ι
.
λ x16 .
λ x17 :
ι → ι
.
0
)
(
λ x15 .
0
)
(
λ x15 :
ι → ι
.
λ x16 .
0
)
(
λ x15 .
0
)
)
0
)
(
λ x12 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
x9
0
)
)
(
λ x9 .
x7
)
(
λ x9 :
ι → ι
.
λ x10 .
setsum
(
x1
(
λ x11 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
λ x12 x13 .
λ x14 :
ι → ι
.
x3
(
λ x15 x16 .
0
)
(
λ x15 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
0
)
)
(
setsum
0
0
)
(
x0
(
λ x11 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
λ x12 :
ι →
ι →
ι → ι
.
λ x13 :
ι → ι
.
0
)
(
λ x11 :
ι → ι
.
λ x12 .
λ x13 :
ι → ι
.
0
)
(
λ x11 .
0
)
(
λ x11 :
ι → ι
.
λ x12 .
0
)
(
λ x11 .
0
)
)
(
x3
(
λ x11 x12 .
0
)
(
λ x11 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
0
)
)
(
λ x11 .
setsum
0
0
)
0
)
(
x9
(
setsum
0
0
)
)
)
(
λ x9 .
0
)
)
(
λ x9 .
x0
(
λ x10 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
λ x11 :
ι →
ι →
ι → ι
.
λ x12 :
ι → ι
.
x10
(
λ x13 x14 x15 .
x14
)
(
λ x13 :
ι → ι
.
setsum
(
x0
(
λ x14 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
λ x15 :
ι →
ι →
ι → ι
.
λ x16 :
ι → ι
.
0
)
(
λ x14 :
ι → ι
.
λ x15 .
λ x16 :
ι → ι
.
0
)
(
λ x14 .
0
)
(
λ x14 :
ι → ι
.
λ x15 .
0
)
(
λ x14 .
0
)
)
(
Inj0
0
)
)
0
)
(
λ x10 :
ι → ι
.
λ x11 .
λ x12 :
ι → ι
.
Inj1
(
setsum
0
(
x10
0
)
)
)
(
λ x10 .
setsum
0
(
Inj0
(
setsum
0
0
)
)
)
(
λ x10 :
ι → ι
.
λ x11 .
x10
0
)
(
λ x10 .
0
)
)
(
x5
(
setsum
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
x7
)
)
=
x5
(
x0
(
λ x9 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
λ x10 :
ι →
ι →
ι → ι
.
λ x11 :
ι → ι
.
x7
)
(
λ x9 :
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
x0
(
λ x12 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
λ x13 :
ι →
ι →
ι → ι
.
λ x14 :
ι → ι
.
x13
(
x14
0
)
(
x0
(
λ x15 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
λ x16 :
ι →
ι →
ι → ι
.
λ x17 :
ι → ι
.
0
)
(
λ x15 :
ι → ι
.
λ x16 .
λ x17 :
ι → ι
.
0
)
(
λ x15 .
0
)
(
λ x15 :
ι → ι
.
λ x16 .
0
)
(
λ x15 .
0
)
)
(
x1
(
λ x15 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
λ x16 x17 .
λ x18 :
ι → ι
.
0
)
0
0
0
(
λ x15 .
0
)
0
)
)
(
λ x12 :
ι → ι
.
λ x13 .
λ x14 :
ι → ι
.
Inj0
0
)
(
λ x12 .
setsum
(
Inj1
0
)
0
)
(
λ x12 :
ι → ι
.
λ x13 .
x12
(
Inj0
0
)
)
(
λ x12 .
x9
0
)
)
(
λ x9 .
0
)
(
λ x9 :
ι → ι
.
λ x10 .
x9
(
Inj0
0
)
)
(
λ x9 .
x6
)
)
)
⟶
(
∀ x4 .
∀ x5 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x6 :
ι → ι
.
∀ x7 .
x0
(
λ x9 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
λ x10 :
ι →
ι →
ι → ι
.
λ x11 :
ι → ι
.
0
)
(
λ x9 :
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
x7
)
(
λ x9 .
Inj0
0
)
(
λ x9 :
ι → ι
.
λ x10 .
Inj0
0
)
(
λ x9 .
x0
(
λ x10 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
λ x11 :
ι →
ι →
ι → ι
.
λ x12 :
ι → ι
.
x2
(
λ x13 .
Inj1
(
Inj0
0
)
)
(
x12
(
setsum
0
0
)
)
)
(
λ x10 :
ι → ι
.
λ x11 .
λ x12 :
ι → ι
.
0
)
(
λ x10 .
x9
)
(
λ x10 :
ι → ι
.
λ x11 .
setsum
(
x3
(
λ x12 x13 .
x10
0
)
(
λ x12 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
x9
)
)
(
setsum
0
(
setsum
0
0
)
)
)
(
λ x10 .
x3
(
λ x11 x12 .
Inj0
(
setsum
0
0
)
)
(
λ x11 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
x10
)
)
)
=
setsum
x4
(
setsum
(
x0
(
λ x9 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
λ x10 :
ι →
ι →
ι → ι
.
λ x11 :
ι → ι
.
0
)
(
λ x9 :
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
Inj0
(
x1
(
λ x12 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
λ x13 x14 .
λ x15 :
ι → ι
.
0
)
0
0
0
(
λ x12 .
0
)
0
)
)
(
λ x9 .
x7
)
(
λ x9 :
ι → ι
.
λ x10 .
setsum
(
Inj0
0
)
(
x6
0
)
)
(
λ x9 .
0
)
)
(
x2
(
λ x9 .
setsum
(
Inj0
0
)
(
x0
(
λ x10 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
λ x11 :
ι →
ι →
ι → ι
.
λ x12 :
ι → ι
.
0
)
(
λ x10 :
ι → ι
.
λ x11 .
λ x12 :
ι → ι
.
0
)
(
λ x10 .
0
)
(
λ x10 :
ι → ι
.
λ x11 .
0
)
(
λ x10 .
0
)
)
)
(
x3
(
λ x9 x10 .
x6
0
)
(
λ x9 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 :
(
(
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x5 x6 x7 .
x0
(
λ x9 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
λ x10 :
ι →
ι →
ι → ι
.
λ x11 :
ι → ι
.
x1
(
λ x12 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
λ x13 x14 .
λ x15 :
ι → ι
.
Inj1
(
x15
x13
)
)
(
Inj0
(
setsum
(
x2
(
λ x12 .
0
)
0
)
0
)
)
0
0
(
λ x12 .
x2
(
λ x13 .
setsum
(
setsum
0
0
)
(
x2
(
λ x14 .
0
)
0
)
)
0
)
x7
)
(
λ x9 :
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
setsum
(
Inj1
(
Inj0
(
x9
0
)
)
)
0
)
(
λ x9 .
setsum
0
(
setsum
x7
(
Inj1
(
x1
(
λ x10 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
λ x11 x12 .
λ x13 :
ι → ι
.
0
)
0
0
0
(
λ x10 .
0
)
0
)
)
)
)
(
λ x9 :
ι → ι
.
λ x10 .
x6
)
(
λ x9 .
x6
)
=
x1
(
λ x9 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
λ x10 x11 .
λ x12 :
ι → ι
.
x12
(
x3
(
λ x13 x14 .
Inj1
0
)
(
λ x13 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
x11
)
)
)
(
setsum
(
setsum
0
x7
)
(
Inj1
x6
)
)
(
Inj1
(
Inj0
(
setsum
(
x0
(
λ x9 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
λ x10 :
ι →
ι →
ι → ι
.
λ x11 :
ι → ι
.
0
)
(
λ x9 :
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
0
)
(
λ x9 .
0
)
(
λ x9 :
ι → ι
.
λ x10 .
0
)
(
λ x9 .
0
)
)
(
setsum
0
0
)
)
)
)
(
Inj0
x7
)
(
λ x9 .
Inj0
0
)
(
setsum
0
(
x4
(
λ x9 :
ι → ι
.
x6
)
(
λ x9 :
ι → ι
.
0
)
)
)
)
⟶
False
(proof)
Theorem
0f506..
:
∀ x0 :
(
ι →
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι →
ι →
ι → ι
)
→
ι → ι
.
∀ x1 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
∀ x2 :
(
(
ι →
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
∀ x3 :
(
ι →
ι → ι
)
→
(
(
ι →
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
(
∀ x4 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x5 :
ι →
ι →
(
ι → ι
)
→ ι
.
∀ x6 x7 :
ι → ι
.
x3
(
λ x9 x10 .
x2
(
λ x11 :
ι →
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
x11
0
(
λ x12 :
ι → ι
.
0
)
(
λ x12 .
x3
(
λ x13 x14 .
x3
(
λ x15 x16 .
0
)
(
λ x15 :
ι →
ι → ι
.
λ x16 :
(
ι → ι
)
→
ι → ι
.
0
)
)
(
λ x13 :
ι →
ι → ι
.
λ x14 :
(
ι → ι
)
→
ι → ι
.
setsum
0
0
)
)
)
(
λ x11 x12 .
Inj0
0
)
)
(
λ x9 :
ι →
ι → ι
.
λ x10 :
(
ι → ι
)
→
ι → ι
.
x9
0
(
x10
(
λ x11 .
setsum
(
x10
(
λ x12 .
0
)
0
)
0
)
(
x7
(
x2
(
λ x11 :
ι →
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
0
)
(
λ x11 x12 .
0
)
)
)
)
)
=
Inj0
0
)
⟶
(
∀ x4 x5 .
∀ x6 :
(
(
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x7 .
x3
(
λ x9 x10 .
x1
(
λ x11 .
x7
)
(
λ x11 :
ι → ι
.
λ x12 .
0
)
(
λ x11 .
x2
(
λ x12 :
ι →
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
0
)
(
λ x12 x13 .
x1
(
λ x14 .
x1
(
λ x15 .
0
)
(
λ x15 :
ι → ι
.
λ x16 .
0
)
(
λ x15 .
0
)
(
λ x15 x16 .
0
)
)
(
λ x14 :
ι → ι
.
λ x15 .
x0
(
λ x16 .
λ x17 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x18 x19 x20 .
0
)
0
)
(
λ x14 .
x0
(
λ x15 .
λ x16 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x17 x18 x19 .
0
)
0
)
(
λ x14 x15 .
Inj0
0
)
)
)
(
λ x11 x12 .
0
)
)
(
λ x9 :
ι →
ι → ι
.
λ x10 :
(
ι → ι
)
→
ι → ι
.
setsum
(
setsum
(
x3
(
λ x11 x12 .
Inj1
0
)
(
λ x11 :
ι →
ι → ι
.
λ x12 :
(
ι → ι
)
→
ι → ι
.
x3
(
λ x13 x14 .
0
)
(
λ x13 :
ι →
ι → ι
.
λ x14 :
(
ι → ι
)
→
ι → ι
.
0
)
)
)
(
x3
(
λ x11 x12 .
x11
)
(
λ x11 :
ι →
ι → ι
.
λ x12 :
(
ι → ι
)
→
ι → ι
.
0
)
)
)
(
setsum
(
x2
(
λ x11 :
ι →
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
Inj0
0
)
(
λ x11 x12 .
setsum
0
0
)
)
(
setsum
0
(
x6
(
λ x11 :
ι → ι
.
0
)
(
λ x11 :
ι → ι
.
0
)
(
λ x11 .
0
)
0
)
)
)
)
=
x1
(
λ x9 .
x6
(
λ x10 :
ι → ι
.
x1
(
λ x11 .
x3
(
λ x12 x13 .
Inj0
0
)
(
λ x12 :
ι →
ι → ι
.
λ x13 :
(
ι → ι
)
→
ι → ι
.
x10
0
)
)
(
λ x11 :
ι → ι
.
λ x12 .
x10
(
setsum
0
0
)
)
(
λ x11 .
setsum
(
x0
(
λ x12 .
λ x13 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x14 x15 x16 .
0
)
0
)
(
x2
(
λ x12 :
ι →
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
0
)
(
λ x12 x13 .
0
)
)
)
(
λ x11 x12 .
0
)
)
(
λ x10 :
ι → ι
.
x2
(
λ x11 :
ι →
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
setsum
x7
(
x11
0
(
λ x12 :
ι → ι
.
0
)
(
λ x12 .
0
)
)
)
(
λ x11 x12 .
x10
(
Inj1
0
)
)
)
(
λ x10 .
0
)
(
x2
(
λ x10 :
ι →
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
0
)
(
λ x10 x11 .
Inj0
0
)
)
)
(
λ x9 :
ι → ι
.
λ x10 .
setsum
(
Inj1
0
)
(
setsum
0
(
x0
(
λ x11 .
λ x12 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x13 x14 x15 .
x15
)
(
x1
(
λ x11 .
0
)
(
λ x11 :
ι → ι
.
λ x12 .
0
)
(
λ x11 .
0
)
(
λ x11 x12 .
0
)
)
)
)
)
(
λ x9 .
x9
)
(
λ x9 x10 .
x9
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
ι → ι
.
∀ x6 x7 .
x2
(
λ x9 :
ι →
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
setsum
(
x2
(
λ x10 :
ι →
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
Inj0
(
x0
(
λ x11 .
λ x12 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x13 x14 x15 .
0
)
0
)
)
(
λ x10 x11 .
0
)
)
(
x2
(
λ x10 :
ι →
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
setsum
(
setsum
0
0
)
(
x2
(
λ x11 :
ι →
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
0
)
(
λ x11 x12 .
0
)
)
)
(
λ x10 x11 .
x1
(
λ x12 .
x0
(
λ x13 .
λ x14 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x15 x16 x17 .
0
)
0
)
(
λ x12 :
ι → ι
.
λ x13 .
setsum
0
0
)
(
λ x12 .
0
)
(
λ x12 x13 .
0
)
)
)
)
(
λ x9 .
setsum
(
Inj1
0
)
)
=
Inj0
(
x0
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 x12 x13 .
x12
)
0
)
)
⟶
(
∀ x4 :
ι →
ι → ι
.
∀ x5 x6 .
∀ x7 :
ι →
(
ι → ι
)
→ ι
.
x2
(
λ x9 :
ι →
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
x5
)
(
λ x9 x10 .
0
)
=
setsum
(
x0
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 x12 x13 .
x2
(
λ x14 :
ι →
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
x14
x12
(
λ x15 :
ι → ι
.
Inj1
0
)
(
λ x15 .
Inj1
0
)
)
(
λ x14 x15 .
x2
(
λ x16 :
ι →
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
x15
)
(
λ x16 x17 .
0
)
)
)
(
setsum
(
setsum
(
Inj0
0
)
(
Inj0
0
)
)
0
)
)
(
x7
(
Inj1
(
x4
0
0
)
)
(
λ x9 .
x2
(
λ x10 :
ι →
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
0
)
(
λ x10 x11 .
x2
(
λ x12 :
ι →
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
x2
(
λ x13 :
ι →
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
0
)
(
λ x13 x14 .
0
)
)
(
λ x12 x13 .
x11
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→ ι
.
∀ x6 :
ι →
ι → ι
.
∀ x7 .
x1
(
λ x9 .
x5
(
λ x10 :
ι →
ι → ι
.
λ x11 :
ι → ι
.
λ x12 .
0
)
(
x0
(
λ x10 .
λ x11 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x12 x13 x14 .
x12
)
0
)
(
λ x10 .
x3
(
λ x11 x12 .
0
)
(
λ x11 :
ι →
ι → ι
.
λ x12 :
(
ι → ι
)
→
ι → ι
.
setsum
(
x2
(
λ x13 :
ι →
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
0
)
(
λ x13 x14 .
0
)
)
(
setsum
0
0
)
)
)
)
(
λ x9 :
ι → ι
.
λ x10 .
x1
(
λ x11 .
setsum
(
Inj0
(
Inj1
0
)
)
0
)
(
λ x11 :
ι → ι
.
λ x12 .
setsum
0
(
Inj1
x12
)
)
(
λ x11 .
x9
(
setsum
(
x1
(
λ x12 .
0
)
(
λ x12 :
ι → ι
.
λ x13 .
0
)
(
λ x12 .
0
)
(
λ x12 x13 .
0
)
)
0
)
)
(
λ x11 x12 .
Inj1
(
x1
(
λ x13 .
Inj1
0
)
(
λ x13 :
ι → ι
.
λ x14 .
x12
)
(
λ x13 .
x3
(
λ x14 x15 .
0
)
(
λ x14 :
ι →
ι → ι
.
λ x15 :
(
ι → ι
)
→
ι → ι
.
0
)
)
(
λ x13 x14 .
x0
(
λ x15 .
λ x16 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x17 x18 x19 .
0
)
0
)
)
)
)
(
λ x9 .
x3
(
λ x10 x11 .
x7
)
(
λ x10 :
ι →
ι → ι
.
λ x11 :
(
ι → ι
)
→
ι → ι
.
Inj0
(
Inj1
(
setsum
0
0
)
)
)
)
(
λ x9 x10 .
x10
)
=
Inj0
(
x3
(
λ x9 x10 .
Inj0
x7
)
(
λ x9 :
ι →
ι → ι
.
λ x10 :
(
ι → ι
)
→
ι → ι
.
0
)
)
)
⟶
(
∀ 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
.
x1
(
λ x9 .
x0
(
λ x10 .
λ x11 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x12 x13 x14 .
0
)
(
setsum
0
0
)
)
(
λ x9 :
ι → ι
.
λ x10 .
Inj1
(
x9
(
x7
(
Inj0
0
)
)
)
)
(
λ x9 .
x9
)
(
λ x9 x10 .
0
)
=
x0
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 x12 x13 .
setsum
(
setsum
x11
x11
)
(
setsum
(
x3
(
λ x14 x15 .
x3
(
λ x16 x17 .
0
)
(
λ x16 :
ι →
ι → ι
.
λ x17 :
(
ι → ι
)
→
ι → ι
.
0
)
)
(
λ x14 :
ι →
ι → ι
.
λ x15 :
(
ι → ι
)
→
ι → ι
.
x2
(
λ x16 :
ι →
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
0
)
(
λ x16 x17 .
0
)
)
)
(
x1
(
λ x14 .
0
)
(
λ x14 :
ι → ι
.
λ x15 .
x2
(
λ x16 :
ι →
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
0
)
(
λ x16 x17 .
0
)
)
(
λ x14 .
x14
)
(
λ x14 x15 .
x1
(
λ x16 .
0
)
(
λ x16 :
ι → ι
.
λ x17 .
0
)
(
λ x16 .
0
)
(
λ x16 x17 .
0
)
)
)
)
)
(
Inj0
(
x3
(
λ x9 x10 .
Inj0
(
x3
(
λ x11 x12 .
0
)
(
λ x11 :
ι →
ι → ι
.
λ x12 :
(
ι → ι
)
→
ι → ι
.
0
)
)
)
(
λ x9 :
ι →
ι → ι
.
λ x10 :
(
ι → ι
)
→
ι → ι
.
Inj0
(
Inj1
0
)
)
)
)
)
⟶
(
∀ x4 :
ι →
(
ι → ι
)
→ ι
.
∀ x5 :
ι →
ι →
ι →
ι → ι
.
∀ x6 x7 .
x0
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 x12 x13 .
Inj0
x11
)
0
=
x5
(
x4
(
setsum
0
(
x2
(
λ x9 :
ι →
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
x2
(
λ x10 :
ι →
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
0
)
(
λ x10 x11 .
0
)
)
(
λ x9 x10 .
x0
(
λ x11 .
λ x12 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x13 x14 x15 .
0
)
0
)
)
)
(
λ x9 .
x5
x7
x9
(
x1
(
λ x10 .
setsum
0
0
)
(
λ x10 :
ι → ι
.
λ x11 .
x3
(
λ x12 x13 .
0
)
(
λ x12 :
ι →
ι → ι
.
λ x13 :
(
ι → ι
)
→
ι → ι
.
0
)
)
(
λ x10 .
x2
(
λ x11 :
ι →
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
0
)
(
λ x11 x12 .
0
)
)
(
λ x10 x11 .
0
)
)
x7
)
)
0
x6
(
x1
(
λ x9 .
setsum
0
0
)
(
λ x9 :
ι → ι
.
λ x10 .
0
)
(
λ x9 .
0
)
(
λ x9 x10 .
x10
)
)
)
⟶
(
∀ x4 :
ι →
ι → ι
.
∀ x5 :
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x6 .
∀ x7 :
(
ι → ι
)
→ ι
.
x0
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 x12 x13 .
0
)
0
=
x7
(
λ x9 .
0
)
)
⟶
False
(proof)
Theorem
3976e..
:
∀ x0 :
(
ι →
ι →
(
ι →
ι → ι
)
→
ι → ι
)
→
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x1 :
(
ι →
ι →
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
∀ x2 :
(
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→
(
ι →
ι → ι
)
→
ι → ι
.
∀ x3 :
(
(
ι → ι
)
→ ι
)
→
(
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 x7 .
x3
(
λ x9 :
ι → ι
.
0
)
(
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
setsum
x7
0
)
=
x6
)
⟶
(
∀ x4 .
∀ x5 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x6 x7 .
x3
(
λ x9 :
ι → ι
.
0
)
(
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
x7
)
=
x7
)
⟶
(
∀ x4 :
ι →
(
ι → ι
)
→
ι → ι
.
∀ x5 :
(
(
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
∀ x6 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x7 .
x2
(
λ x9 .
x2
(
λ x10 .
x7
)
(
λ x10 :
ι → ι
.
x3
(
λ x11 :
ι → ι
.
x1
(
λ x12 x13 .
λ x14 :
(
ι → ι
)
→
ι → ι
.
λ x15 :
ι → ι
.
λ x16 .
0
)
x7
)
(
λ x11 :
ι →
(
ι → ι
)
→
ι → ι
.
setsum
0
(
Inj0
0
)
)
)
(
λ x10 x11 .
x2
(
λ x12 .
x2
(
λ x13 .
x11
)
(
λ x13 :
ι → ι
.
setsum
0
0
)
(
λ x13 x14 .
0
)
(
λ x13 x14 .
0
)
0
)
(
λ x12 :
ι → ι
.
Inj1
0
)
(
λ x12 x13 .
0
)
(
λ x12 x13 .
x1
(
λ x14 x15 .
λ x16 :
(
ι → ι
)
→
ι → ι
.
λ x17 :
ι → ι
.
λ x18 .
x0
(
λ x19 x20 .
λ x21 :
ι →
ι → ι
.
λ x22 .
0
)
0
(
λ x19 :
ι → ι
.
0
)
)
(
x0
(
λ x14 x15 .
λ x16 :
ι →
ι → ι
.
λ x17 .
0
)
0
(
λ x14 :
ι → ι
.
0
)
)
)
x7
)
(
λ x10 x11 .
Inj0
(
setsum
x9
(
setsum
0
0
)
)
)
x7
)
(
λ x9 :
ι → ι
.
x9
(
Inj1
(
setsum
0
(
setsum
0
0
)
)
)
)
(
λ x9 x10 .
0
)
(
λ x9 x10 .
x0
(
λ x11 x12 .
λ x13 :
ι →
ι → ι
.
λ x14 .
0
)
x7
(
λ x11 :
ι → ι
.
0
)
)
(
x5
(
λ x9 x10 :
ι → ι
.
setsum
(
x1
(
λ x11 x12 .
λ x13 :
(
ι → ι
)
→
ι → ι
.
λ x14 :
ι → ι
.
λ x15 .
Inj1
0
)
(
x9
0
)
)
x7
)
)
=
x5
(
λ x9 x10 :
ι → ι
.
x9
(
Inj1
(
Inj0
(
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x5 :
(
(
ι →
ι → ι
)
→ ι
)
→
ι → ι
.
∀ x6 :
ι → ι
.
∀ x7 :
(
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
x2
(
λ x9 .
x2
(
λ x10 .
x10
)
(
λ x10 :
ι → ι
.
Inj0
(
x0
(
λ x11 x12 .
λ x13 :
ι →
ι → ι
.
λ x14 .
x13
0
0
)
(
x0
(
λ x11 x12 .
λ x13 :
ι →
ι → ι
.
λ x14 .
0
)
0
(
λ x11 :
ι → ι
.
0
)
)
(
λ x11 :
ι → ι
.
Inj1
0
)
)
)
(
λ x10 x11 .
0
)
(
λ x10 x11 .
x2
(
λ x12 .
0
)
(
λ x12 :
ι → ι
.
x10
)
(
λ x12 x13 .
x0
(
λ x14 x15 .
λ x16 :
ι →
ι → ι
.
λ x17 .
Inj1
0
)
x13
(
λ x14 :
ι → ι
.
0
)
)
(
λ x12 x13 .
0
)
0
)
(
Inj1
0
)
)
(
λ x9 :
ι → ι
.
Inj1
0
)
(
λ x9 x10 .
x2
(
λ x11 .
x11
)
(
λ x11 :
ι → ι
.
0
)
(
λ x11 x12 .
x2
(
λ x13 .
0
)
(
λ x13 :
ι → ι
.
x12
)
(
λ x13 x14 .
x0
(
λ x15 x16 .
λ x17 :
ι →
ι → ι
.
λ x18 .
x15
)
(
x2
(
λ x15 .
0
)
(
λ x15 :
ι → ι
.
0
)
(
λ x15 x16 .
0
)
(
λ x15 x16 .
0
)
0
)
(
λ x15 :
ι → ι
.
x15
0
)
)
(
λ x13 x14 .
x0
(
λ x15 x16 .
λ x17 :
ι →
ι → ι
.
λ x18 .
x18
)
0
(
λ x15 :
ι → ι
.
x1
(
λ x16 x17 .
λ x18 :
(
ι → ι
)
→
ι → ι
.
λ x19 :
ι → ι
.
λ x20 .
0
)
0
)
)
x11
)
(
λ x11 x12 .
0
)
0
)
(
λ x9 x10 .
x9
)
(
x6
(
setsum
0
(
setsum
(
x0
(
λ x9 x10 .
λ x11 :
ι →
ι → ι
.
λ x12 .
0
)
0
(
λ x9 :
ι → ι
.
0
)
)
0
)
)
)
=
x2
(
λ x9 .
Inj0
(
x2
(
λ x10 .
x10
)
(
λ x10 :
ι → ι
.
x2
(
λ x11 .
x9
)
(
λ x11 :
ι → ι
.
x10
0
)
(
λ x11 x12 .
x11
)
(
λ x11 x12 .
x12
)
0
)
(
λ x10 x11 .
Inj1
0
)
(
λ x10 x11 .
setsum
0
(
x2
(
λ x12 .
0
)
(
λ x12 :
ι → ι
.
0
)
(
λ x12 x13 .
0
)
(
λ x12 x13 .
0
)
0
)
)
0
)
)
(
λ x9 :
ι → ι
.
setsum
0
0
)
(
λ x9 x10 .
setsum
0
(
x3
(
λ x11 :
ι → ι
.
x10
)
(
λ x11 :
ι →
(
ι → ι
)
→
ι → ι
.
x0
(
λ x12 x13 .
λ x14 :
ι →
ι → ι
.
λ x15 .
setsum
0
0
)
(
Inj0
0
)
(
λ x12 :
ι → ι
.
x11
0
(
λ x13 .
0
)
0
)
)
)
)
(
λ x9 x10 .
x7
(
λ x11 .
Inj0
(
Inj1
0
)
)
(
λ x11 :
ι → ι
.
Inj0
x10
)
0
)
(
x6
(
x0
(
λ x9 x10 .
λ x11 :
ι →
ι → ι
.
λ x12 .
0
)
(
setsum
(
setsum
0
0
)
(
x7
(
λ x9 .
0
)
(
λ x9 :
ι → ι
.
0
)
0
)
)
(
λ x9 :
ι → ι
.
0
)
)
)
)
⟶
(
∀ x4 x5 x6 x7 .
x1
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
setsum
x13
0
)
(
x1
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
x1
(
λ x14 x15 .
λ x16 :
(
ι → ι
)
→
ι → ι
.
λ x17 :
ι → ι
.
λ x18 .
0
)
(
setsum
0
(
setsum
0
0
)
)
)
(
setsum
(
x2
(
λ x9 .
setsum
0
0
)
(
λ x9 :
ι → ι
.
setsum
0
0
)
(
λ x9 x10 .
x10
)
(
λ x9 x10 .
x0
(
λ x11 x12 .
λ x13 :
ι →
ι → ι
.
λ x14 .
0
)
0
(
λ x11 :
ι → ι
.
0
)
)
0
)
0
)
)
=
x1
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
Inj0
(
x12
(
setsum
(
Inj1
0
)
x10
)
)
)
(
Inj1
0
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
ι →
(
ι → ι
)
→ ι
.
∀ x6 x7 .
x1
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
0
)
x4
=
setsum
(
setsum
(
x2
(
λ x9 .
0
)
(
λ x9 :
ι → ι
.
setsum
(
x0
(
λ x10 x11 .
λ x12 :
ι →
ι → ι
.
λ x13 .
0
)
0
(
λ x10 :
ι → ι
.
0
)
)
(
x1
(
λ x10 x11 .
λ x12 :
(
ι → ι
)
→
ι → ι
.
λ x13 :
ι → ι
.
λ x14 .
0
)
0
)
)
(
λ x9 x10 .
x9
)
(
λ x9 x10 .
Inj1
x6
)
(
Inj1
0
)
)
0
)
0
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
ι →
ι →
ι → ι
.
x0
(
λ x9 x10 .
λ x11 :
ι →
ι → ι
.
λ x12 .
x1
(
λ x13 x14 .
λ x15 :
(
ι → ι
)
→
ι → ι
.
λ x16 :
ι → ι
.
λ x17 .
0
)
(
x0
(
λ x13 x14 .
λ x15 :
ι →
ι → ι
.
λ x16 .
0
)
x12
(
λ x13 :
ι → ι
.
x11
0
0
)
)
)
(
x2
(
λ x9 .
x3
(
λ x10 :
ι → ι
.
x10
x9
)
(
λ x10 :
ι →
(
ι → ι
)
→
ι → ι
.
x3
(
λ x11 :
ι → ι
.
x7
0
0
0
)
(
λ x11 :
ι →
(
ι → ι
)
→
ι → ι
.
x0
(
λ x12 x13 .
λ x14 :
ι →
ι → ι
.
λ x15 .
0
)
0
(
λ x12 :
ι → ι
.
0
)
)
)
)
(
λ x9 :
ι → ι
.
Inj1
(
x9
(
Inj0
0
)
)
)
(
λ x9 x10 .
x7
x10
(
x0
(
λ x11 x12 .
λ x13 :
ι →
ι → ι
.
λ x14 .
x11
)
(
x0
(
λ x11 x12 .
λ x13 :
ι →
ι → ι
.
λ x14 .
0
)
0
(
λ x11 :
ι → ι
.
0
)
)
(
λ x11 :
ι → ι
.
setsum
0
0
)
)
0
)
(
λ x9 x10 .
0
)
(
Inj1
(
x0
(
λ x9 x10 .
λ x11 :
ι →
ι → ι
.
λ x12 .
Inj1
0
)
0
(
λ x9 :
ι → ι
.
x9
0
)
)
)
)
(
λ x9 :
ι → ι
.
x5
)
=
x1
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
x1
(
λ x14 x15 .
λ x16 :
(
ι → ι
)
→
ι → ι
.
λ x17 :
ι → ι
.
λ x18 .
0
)
(
setsum
0
(
x12
(
setsum
0
0
)
)
)
)
(
setsum
x4
0
)
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
ι →
(
ι → ι
)
→ ι
.
x0
(
λ x9 x10 .
λ x11 :
ι →
ι → ι
.
λ x12 .
x0
(
λ x13 x14 .
λ x15 :
ι →
ι → ι
.
λ x16 .
x2
(
λ x17 .
x2
(
λ x18 .
x15
0
0
)
(
λ x18 :
ι → ι
.
setsum
0
0
)
(
λ x18 x19 .
x3
(
λ x20 :
ι → ι
.
0
)
(
λ x20 :
ι →
(
ι → ι
)
→
ι → ι
.
0
)
)
(
λ x18 x19 .
0
)
0
)
(
λ x17 :
ι → ι
.
Inj1
(
setsum
0
0
)
)
(
λ x17 x18 .
x15
x18
(
x1
(
λ x19 x20 .
λ x21 :
(
ι → ι
)
→
ι → ι
.
λ x22 :
ι → ι
.
λ x23 .
0
)
0
)
)
(
λ x17 x18 .
x3
(
λ x19 :
ι → ι
.
x3
(
λ x20 :
ι → ι
.
0
)
(
λ x20 :
ι →
(
ι → ι
)
→
ι → ι
.
0
)
)
(
λ x19 :
ι →
(
ι → ι
)
→
ι → ι
.
x2
(
λ x20 .
0
)
(
λ x20 :
ι → ι
.
0
)
(
λ x20 x21 .
0
)
(
λ x20 x21 .
0
)
0
)
)
0
)
(
x1
(
λ x13 x14 .
λ x15 :
(
ι → ι
)
→
ι → ι
.
λ x16 :
ι → ι
.
λ x17 .
x15
(
λ x18 .
setsum
0
0
)
0
)
x10
)
(
λ x13 :
ι → ι
.
setsum
(
x2
(
λ x14 .
x13
0
)
(
λ x14 :
ι → ι
.
x0
(
λ x15 x16 .
λ x17 :
ι →
ι → ι
.
λ x18 .
0
)
0
(
λ x15 :
ι → ι
.
0
)
)
(
λ x14 x15 .
0
)
(
λ x14 x15 .
x15
)
x12
)
(
Inj0
x12
)
)
)
(
setsum
0
0
)
(
λ x9 :
ι → ι
.
x6
)
=
x0
(
λ x9 x10 .
λ x11 :
ι →
ι → ι
.
λ x12 .
Inj1
(
setsum
(
Inj1
(
x3
(
λ x13 :
ι → ι
.
0
)
(
λ x13 :
ι →
(
ι → ι
)
→
ι → ι
.
0
)
)
)
x12
)
)
(
setsum
(
Inj0
0
)
0
)
(
λ x9 :
ι → ι
.
setsum
(
x7
(
x1
(
λ x10 x11 .
λ x12 :
(
ι → ι
)
→
ι → ι
.
λ x13 :
ι → ι
.
λ x14 .
0
)
(
setsum
0
0
)
)
(
λ x10 .
x3
(
λ x11 :
ι → ι
.
0
)
(
λ x11 :
ι →
(
ι → ι
)
→
ι → ι
.
x1
(
λ x12 x13 .
λ x14 :
(
ι → ι
)
→
ι → ι
.
λ x15 :
ι → ι
.
λ x16 .
0
)
0
)
)
)
(
setsum
x6
x5
)
)
)
⟶
False
(proof)
Theorem
078d5..
:
∀ x0 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
∀ x1 :
(
(
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
)
→
ι → ι
.
∀ x2 :
(
ι →
ι →
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
.
∀ x3 :
(
ι →
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι →
ι → ι
)
→
ι → ι
.
(
∀ x4 :
ι →
ι → ι
.
∀ x5 .
∀ x6 :
ι → ι
.
∀ x7 .
x3
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x11 :
ι → ι
.
λ x12 x13 .
0
)
0
=
Inj1
(
Inj1
(
x4
(
x3
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x11 :
ι → ι
.
λ x12 x13 .
Inj1
0
)
(
setsum
0
0
)
)
(
x3
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x11 :
ι → ι
.
λ x12 x13 .
Inj1
0
)
x5
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
ι → ι
.
∀ x6 x7 .
x3
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x11 :
ι → ι
.
λ x12 x13 .
0
)
0
=
x4
)
⟶
(
∀ x4 x5 :
ι → ι
.
∀ x6 :
(
ι → ι
)
→
ι → ι
.
∀ x7 :
(
ι →
ι → ι
)
→ ι
.
x2
(
λ x9 x10 x11 .
λ x12 :
ι → ι
.
x10
)
0
=
setsum
(
Inj1
(
x6
(
λ x9 .
0
)
(
x7
(
λ x9 x10 .
Inj0
0
)
)
)
)
0
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 x6 x7 .
x2
(
λ x9 x10 x11 .
λ x12 :
ι → ι
.
x2
(
λ x13 x14 x15 .
λ x16 :
ι → ι
.
x1
(
λ x17 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
x15
)
0
)
(
x1
(
λ x13 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
x11
)
0
)
)
x7
=
x7
)
⟶
(
∀ x4 x5 x6 x7 .
x1
(
λ x9 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
x0
(
λ x10 .
λ x11 :
ι → ι
.
x3
(
λ x12 .
λ x13 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x14 :
ι → ι
.
λ x15 x16 .
setsum
0
0
)
(
x3
(
λ x12 .
λ x13 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x14 :
ι → ι
.
λ x15 x16 .
x16
)
0
)
)
0
(
Inj1
0
)
)
0
=
setsum
0
0
)
⟶
(
∀ x4 x5 x6 x7 .
x1
(
λ x9 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
x6
)
(
setsum
(
x2
(
λ x9 x10 x11 .
λ x12 :
ι → ι
.
x0
(
λ x13 .
λ x14 :
ι → ι
.
0
)
(
setsum
0
0
)
x11
)
0
)
x6
)
=
x6
)
⟶
(
∀ x4 :
ι →
ι →
ι →
ι → ι
.
∀ x5 .
∀ x6 :
ι → ι
.
∀ x7 .
x0
(
λ x9 .
λ x10 :
ι → ι
.
0
)
(
Inj1
(
x4
(
Inj1
0
)
0
(
setsum
(
x6
0
)
(
x1
(
λ x9 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
0
)
)
0
)
)
(
x0
(
λ x9 .
λ x10 :
ι → ι
.
x7
)
(
x4
(
x1
(
λ x9 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
x7
)
(
setsum
0
0
)
)
(
setsum
(
x6
0
)
0
)
0
(
Inj0
(
Inj0
0
)
)
)
(
Inj1
x7
)
)
=
setsum
0
0
)
⟶
(
∀ x4 :
ι →
ι →
ι →
ι → ι
.
∀ x5 :
ι →
(
ι →
ι → ι
)
→ ι
.
∀ x6 :
(
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x7 :
ι →
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
x0
(
λ x9 .
λ x10 :
ι → ι
.
x3
(
λ x11 .
λ x12 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x13 :
ι → ι
.
λ x14 x15 .
x1
(
λ x16 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
x15
)
0
)
(
x0
(
λ x11 .
λ x12 :
ι → ι
.
setsum
0
0
)
(
setsum
0
(
Inj0
0
)
)
(
x0
(
λ x11 .
λ x12 :
ι → ι
.
0
)
(
setsum
0
0
)
0
)
)
)
0
(
x0
(
λ x9 .
λ x10 :
ι → ι
.
setsum
(
x3
(
λ x11 .
λ x12 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x13 :
ι → ι
.
λ x14 x15 .
0
)
(
x2
(
λ x11 x12 x13 .
λ x14 :
ι → ι
.
0
)
0
)
)
(
x7
(
x6
(
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 x13 .
0
)
(
λ x11 :
ι → ι
.
0
)
)
(
λ x11 :
ι → ι
.
0
)
(
setsum
0
0
)
(
x6
(
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 x13 .
0
)
(
λ x11 :
ι → ι
.
0
)
)
)
)
(
x5
(
x0
(
λ x9 .
λ x10 :
ι → ι
.
x10
0
)
0
(
x4
0
0
0
0
)
)
(
λ x9 x10 .
x1
(
λ x11 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
x3
(
λ x12 .
λ x13 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x14 :
ι → ι
.
λ x15 x16 .
0
)
0
)
0
)
)
0
)
=
x3
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x11 :
ι → ι
.
λ x12 x13 .
x13
)
(
Inj0
(
x1
(
λ x9 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
(
x7
0
(
λ x9 :
ι → ι
.
0
)
(
x4
0
0
0
0
)
(
Inj1
0
)
)
)
)
)
⟶
False
(proof)
Theorem
1ed11..
:
∀ x0 :
(
ι → ι
)
→
ι → ι
.
∀ x1 :
(
ι →
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
.
∀ x2 :
(
ι →
ι →
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
)
→
(
ι →
ι →
ι →
ι → ι
)
→ ι
.
∀ x3 :
(
(
(
ι →
ι → ι
)
→ ι
)
→ ι
)
→
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
(
∀ x4 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
∀ x5 x6 .
∀ x7 :
ι →
(
ι → ι
)
→ ι
.
x3
(
λ x9 :
(
ι →
ι → ι
)
→ ι
.
setsum
(
x1
(
λ x10 x11 .
λ x12 :
ι → ι
.
Inj0
x10
)
(
x3
(
λ x10 :
(
ι →
ι → ι
)
→ ι
.
x0
(
λ x11 .
0
)
0
)
(
λ x10 .
λ x11 :
ι → ι
.
x9
(
λ x12 x13 .
0
)
)
)
)
(
Inj0
(
x0
(
λ x10 .
0
)
0
)
)
)
(
λ x9 .
λ x10 :
ι → ι
.
0
)
=
setsum
(
Inj0
(
Inj0
(
setsum
x6
(
setsum
0
0
)
)
)
)
x6
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 .
∀ x6 :
ι → ι
.
∀ x7 .
x3
(
λ x9 :
(
ι →
ι → ι
)
→ ι
.
x6
(
x2
(
λ x10 x11 .
λ x12 :
(
ι → ι
)
→ ι
.
λ x13 :
ι → ι
.
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
(
λ x10 x11 x12 x13 .
0
)
)
)
(
λ x9 .
λ x10 :
ι → ι
.
Inj0
0
)
=
x6
(
x3
(
λ x9 :
(
ι →
ι → ι
)
→ ι
.
Inj0
0
)
(
λ x9 .
λ x10 :
ι → ι
.
0
)
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
ι →
ι →
ι → ι
.
∀ x6 :
(
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
∀ x7 .
x2
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 :
ι → ι
.
x9
)
(
λ x9 x10 x11 x12 .
x3
(
λ x13 :
(
ι →
ι → ι
)
→ ι
.
x2
(
λ x14 x15 .
λ x16 :
(
ι → ι
)
→ ι
.
λ x17 :
ι → ι
.
0
)
(
λ x14 x15 x16 x17 .
x0
(
λ x18 .
Inj0
0
)
(
Inj1
0
)
)
)
(
λ x13 .
λ x14 :
ι → ι
.
x2
(
λ x15 x16 .
λ x17 :
(
ι → ι
)
→ ι
.
λ x18 :
ι → ι
.
Inj0
(
Inj0
0
)
)
(
λ x15 x16 x17 x18 .
x17
)
)
)
=
Inj1
(
x3
(
λ x9 :
(
ι →
ι → ι
)
→ ι
.
x3
(
λ x10 :
(
ι →
ι → ι
)
→ ι
.
setsum
(
x1
(
λ x11 x12 .
λ x13 :
ι → ι
.
0
)
0
)
(
x0
(
λ x11 .
0
)
0
)
)
(
λ x10 .
λ x11 :
ι → ι
.
x11
(
x0
(
λ x12 .
0
)
0
)
)
)
(
λ x9 .
λ x10 :
ι → ι
.
x0
(
λ x11 .
0
)
(
setsum
(
x6
(
λ x11 x12 :
ι → ι
.
λ x13 .
0
)
0
)
0
)
)
)
)
⟶
(
∀ x4 x5 x6 x7 .
x2
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 :
ι → ι
.
setsum
(
x0
(
λ x13 .
x3
(
λ x14 :
(
ι →
ι → ι
)
→ ι
.
x1
(
λ x15 x16 .
λ x17 :
ι → ι
.
0
)
0
)
(
λ x14 .
λ x15 :
ι → ι
.
x13
)
)
(
setsum
0
(
setsum
0
0
)
)
)
(
x12
(
setsum
0
0
)
)
)
(
λ x9 x10 x11 x12 .
Inj0
(
setsum
(
setsum
(
Inj1
0
)
x9
)
0
)
)
=
x4
)
⟶
(
∀ x4 x5 x6 x7 .
x1
(
λ x9 x10 .
λ x11 :
ι → ι
.
x1
(
λ x12 x13 .
λ x14 :
ι → ι
.
0
)
x7
)
x6
=
x1
(
λ x9 x10 .
λ x11 :
ι → ι
.
Inj1
(
x1
(
λ x12 x13 .
λ x14 :
ι → ι
.
setsum
(
setsum
0
0
)
(
x2
(
λ x15 x16 .
λ x17 :
(
ι → ι
)
→ ι
.
λ x18 :
ι → ι
.
0
)
(
λ x15 x16 x17 x18 .
0
)
)
)
x7
)
)
(
setsum
0
0
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→
ι →
ι → ι
.
∀ x5 x6 .
∀ x7 :
(
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
x1
(
λ x9 x10 .
λ x11 :
ι → ι
.
x10
)
(
x2
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 :
ι → ι
.
0
)
(
λ x9 x10 x11 x12 .
Inj0
(
setsum
x10
(
x3
(
λ x13 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x13 .
λ x14 :
ι → ι
.
0
)
)
)
)
)
=
Inj0
x6
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 :
(
(
ι →
ι → ι
)
→ ι
)
→ ι
.
∀ x7 .
x0
(
λ x9 .
setsum
0
(
Inj1
x7
)
)
(
x3
(
λ x9 :
(
ι →
ι → ι
)
→ ι
.
x6
(
λ x10 :
ι →
ι → ι
.
Inj1
(
x3
(
λ x11 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x11 .
λ x12 :
ι → ι
.
0
)
)
)
)
(
λ x9 .
λ x10 :
ι → ι
.
setsum
(
x2
(
λ x11 x12 .
λ x13 :
(
ι → ι
)
→ ι
.
λ x14 :
ι → ι
.
Inj0
0
)
(
λ x11 x12 x13 x14 .
x3
(
λ x15 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x15 .
λ x16 :
ι → ι
.
0
)
)
)
0
)
)
=
Inj0
(
setsum
0
(
x2
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 :
ι → ι
.
0
)
(
λ x9 x10 x11 x12 .
x9
)
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x6 .
∀ x7 :
(
ι → ι
)
→ ι
.
x0
(
λ x9 .
x3
(
λ x10 :
(
ι →
ι → ι
)
→ ι
.
setsum
0
0
)
(
λ x10 .
λ x11 :
ι → ι
.
setsum
x9
0
)
)
(
x3
(
λ x9 :
(
ι →
ι → ι
)
→ ι
.
setsum
0
(
x5
(
λ x10 .
λ x11 :
ι → ι
.
λ x12 .
0
)
)
)
(
λ x9 .
λ x10 :
ι → ι
.
x3
(
λ x11 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x11 .
λ x12 :
ι → ι
.
x1
(
λ x13 x14 .
λ x15 :
ι → ι
.
x3
(
λ x16 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x16 .
λ x17 :
ι → ι
.
0
)
)
(
setsum
0
0
)
)
)
)
=
setsum
(
Inj1
(
x2
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 :
ι → ι
.
0
)
(
λ x9 x10 x11 x12 .
x3
(
λ x13 :
(
ι →
ι → ι
)
→ ι
.
x10
)
(
λ x13 .
λ x14 :
ι → ι
.
x2
(
λ x15 x16 .
λ x17 :
(
ι → ι
)
→ ι
.
λ x18 :
ι → ι
.
0
)
(
λ x15 x16 x17 x18 .
0
)
)
)
)
)
(
x5
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 .
Inj0
(
x3
(
λ x12 :
(
ι →
ι → ι
)
→ ι
.
x1
(
λ x13 x14 .
λ x15 :
ι → ι
.
0
)
0
)
(
λ x12 .
λ x13 :
ι → ι
.
x3
(
λ x14 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
λ x14 .
λ x15 :
ι → ι
.
0
)
)
)
)
)
)
⟶
False
(proof)
Theorem
11c22..
:
∀ x0 :
(
(
ι →
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→ ι
)
→
ι → ι
.
∀ x1 :
(
ι → ι
)
→
(
(
ι →
ι →
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
)
→ ι
.
∀ x2 :
(
(
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
)
→
ι → ι
)
→
ι →
(
ι →
ι →
ι → ι
)
→ ι
.
∀ x3 :
(
(
ι →
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
(
ι →
(
ι → ι
)
→
ι → ι
)
→
ι →
ι →
ι → ι
)
→ ι
.
(
∀ x4 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x5 :
(
(
ι →
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x6 :
(
ι → ι
)
→ ι
.
∀ x7 :
ι → ι
.
x3
(
λ x9 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
x1
(
λ x10 .
x0
(
λ x11 :
ι →
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
x11
(
x1
(
λ x12 .
0
)
(
λ x12 :
ι →
ι →
ι → ι
.
λ x13 :
ι →
ι → ι
.
0
)
)
(
λ x12 :
ι → ι
.
setsum
0
0
)
(
x2
(
λ x12 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
λ x13 .
0
)
0
(
λ x12 x13 x14 .
0
)
)
)
(
Inj0
(
x7
0
)
)
)
(
λ x10 :
ι →
ι →
ι → ι
.
λ x11 :
ι →
ι → ι
.
0
)
)
(
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x10 x11 x12 .
setsum
(
setsum
(
x3
(
λ x13 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
x1
(
λ x14 .
0
)
(
λ x14 :
ι →
ι →
ι → ι
.
λ x15 :
ι →
ι → ι
.
0
)
)
(
λ x13 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x14 x15 x16 .
setsum
0
0
)
)
0
)
(
x0
(
λ x13 :
ι →
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
setsum
x12
0
)
(
Inj1
(
setsum
0
0
)
)
)
)
=
x1
(
λ x9 .
x5
(
λ x10 :
ι →
ι → ι
.
λ x11 .
x2
(
λ x12 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
λ x13 .
0
)
x9
(
λ x12 x13 x14 .
x14
)
)
)
(
λ x9 :
ι →
ι →
ι → ι
.
λ x10 :
ι →
ι → ι
.
setsum
0
(
x6
(
λ x11 .
0
)
)
)
)
⟶
(
∀ x4 :
ι →
ι →
ι → ι
.
∀ x5 :
(
ι → ι
)
→ ι
.
∀ x6 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
∀ x7 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
x3
(
λ x9 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
Inj0
(
x5
(
λ x10 .
0
)
)
)
(
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x10 x11 x12 .
x11
)
=
setsum
(
x6
(
λ x9 .
λ x10 :
ι → ι
.
x2
(
λ x11 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
λ x12 .
Inj0
(
x10
0
)
)
(
Inj1
(
x6
(
λ x11 .
λ x12 :
ι → ι
.
0
)
)
)
(
λ x11 x12 x13 .
Inj0
(
Inj1
0
)
)
)
)
0
)
⟶
(
∀ x4 :
ι →
ι → ι
.
∀ x5 .
∀ x6 :
(
ι →
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
∀ x7 .
x2
(
λ x9 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
λ x10 .
setsum
(
x9
(
λ x11 :
(
ι → ι
)
→
ι → ι
.
x10
)
)
(
x1
(
λ x11 .
x10
)
(
λ x11 :
ι →
ι →
ι → ι
.
λ x12 :
ι →
ι → ι
.
setsum
0
(
x1
(
λ x13 .
0
)
(
λ x13 :
ι →
ι →
ι → ι
.
λ x14 :
ι →
ι → ι
.
0
)
)
)
)
)
0
(
λ x9 x10 x11 .
0
)
=
Inj1
(
x2
(
λ x9 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
λ x10 .
x0
(
λ x11 :
ι →
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
x0
(
λ x12 :
ι →
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
0
)
(
x9
(
λ x12 :
(
ι → ι
)
→
ι → ι
.
0
)
)
)
0
)
(
x6
(
λ x9 x10 .
x0
(
λ x11 :
ι →
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
0
)
(
Inj0
0
)
)
(
λ x9 :
ι → ι
.
λ x10 .
setsum
0
x7
)
(
x4
(
Inj1
0
)
(
x0
(
λ x9 :
ι →
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
0
)
0
)
)
)
(
λ x9 x10 x11 .
x11
)
)
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 .
∀ x7 :
ι → ι
.
x2
(
λ x9 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
λ x10 .
setsum
(
x2
(
λ x11 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
λ x12 .
x11
(
λ x13 :
(
ι → ι
)
→
ι → ι
.
x13
(
λ x14 .
0
)
0
)
)
x10
(
λ x11 x12 x13 .
x3
(
λ x14 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
x2
(
λ x15 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
λ x16 .
0
)
0
(
λ x15 x16 x17 .
0
)
)
(
λ x14 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x15 x16 x17 .
x17
)
)
)
(
x1
(
λ x11 .
x1
(
λ x12 .
0
)
(
λ x12 :
ι →
ι →
ι → ι
.
λ x13 :
ι →
ι → ι
.
x11
)
)
(
λ x11 :
ι →
ι →
ι → ι
.
λ x12 :
ι →
ι → ι
.
setsum
(
x12
0
0
)
(
x11
0
0
0
)
)
)
)
(
x0
(
λ x9 :
ι →
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
Inj0
x6
)
(
setsum
0
(
x0
(
λ x9 :
ι →
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
x0
(
λ x10 :
ι →
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
0
)
0
)
(
x2
(
λ x9 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
λ x10 .
0
)
0
(
λ x9 x10 x11 .
0
)
)
)
)
)
(
λ x9 x10 x11 .
x10
)
=
Inj1
(
setsum
0
0
)
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
ι → ι
.
x1
(
λ x9 .
0
)
(
λ x9 :
ι →
ι →
ι → ι
.
λ x10 :
ι →
ι → ι
.
x7
(
x0
(
λ x11 :
ι →
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
0
)
0
)
)
=
x7
(
Inj0
(
x7
(
x1
(
λ x9 .
0
)
(
λ x9 :
ι →
ι →
ι → ι
.
λ x10 :
ι →
ι → ι
.
x10
0
0
)
)
)
)
)
⟶
(
∀ x4 x5 x6 x7 .
x1
(
λ x9 .
setsum
(
x3
(
λ x10 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
Inj0
(
x2
(
λ x11 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
λ x12 .
0
)
0
(
λ x11 x12 x13 .
0
)
)
)
(
λ x10 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x11 x12 x13 .
x0
(
λ x14 :
ι →
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
setsum
0
0
)
0
)
)
x6
)
(
λ x9 :
ι →
ι →
ι → ι
.
λ x10 :
ι →
ι → ι
.
Inj0
0
)
=
x6
)
⟶
(
∀ x4 .
∀ x5 :
(
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
∀ x6 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→
ι →
ι → ι
.
∀ x7 .
x0
(
λ x9 :
ι →
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
x3
(
λ x10 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x10 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x11 x12 x13 .
0
)
)
(
x2
(
λ x9 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
λ x10 .
x1
(
λ x11 .
0
)
(
λ x11 :
ι →
ι →
ι → ι
.
λ x12 :
ι →
ι → ι
.
x0
(
λ x13 :
ι →
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
x1
(
λ x14 .
0
)
(
λ x14 :
ι →
ι →
ι → ι
.
λ x15 :
ι →
ι → ι
.
0
)
)
(
x1
(
λ x13 .
0
)
(
λ x13 :
ι →
ι →
ι → ι
.
λ x14 :
ι →
ι → ι
.
0
)
)
)
)
0
(
λ x9 x10 x11 .
0
)
)
=
setsum
(
x3
(
λ x9 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
x1
(
λ x10 .
0
)
(
λ x10 :
ι →
ι →
ι → ι
.
λ x11 :
ι →
ι → ι
.
0
)
)
(
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x10 x11 x12 .
setsum
0
(
x2
(
λ x13 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
λ x14 .
0
)
(
x2
(
λ x13 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
λ x14 .
0
)
0
(
λ x13 x14 x15 .
0
)
)
(
λ x13 x14 x15 .
x13
)
)
)
)
0
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 .
∀ x6 :
ι → ι
.
∀ x7 .
x0
(
λ x9 :
ι →
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
0
)
0
=
x7
)
⟶
False
(proof)
Theorem
9d79e..
:
∀ x0 :
(
ι →
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→
ι → ι
.
∀ x1 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→
(
ι → ι
)
→
(
ι →
ι → ι
)
→
ι →
ι → ι
.
∀ x2 :
(
(
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι → ι
)
→
ι →
(
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
∀ x3 :
(
ι →
ι → ι
)
→
ι →
ι →
ι → ι
.
(
∀ x4 x5 x6 .
∀ x7 :
(
ι → ι
)
→
ι →
ι → ι
.
x3
(
λ x9 x10 .
0
)
0
(
x2
(
λ x9 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 .
0
)
(
x2
(
λ x9 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 .
x6
)
x6
(
λ x9 :
ι →
ι → ι
.
λ x10 x11 .
0
)
)
(
λ x9 :
ι →
ι → ι
.
λ x10 x11 .
x1
(
λ x12 x13 .
Inj0
0
)
(
λ x12 .
x12
)
(
λ x12 .
0
)
(
λ x12 x13 .
0
)
(
setsum
(
Inj0
0
)
(
x1
(
λ x12 x13 .
0
)
(
λ x12 .
0
)
(
λ x12 .
0
)
(
λ x12 x13 .
0
)
0
0
)
)
(
x3
(
λ x12 x13 .
0
)
x10
x11
(
x2
(
λ x12 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x13 .
0
)
0
(
λ x12 :
ι →
ι → ι
.
λ x13 x14 .
0
)
)
)
)
)
(
x7
(
λ x9 .
x6
)
x4
0
)
=
x7
(
λ x9 .
x7
(
λ x10 .
x6
)
(
x0
(
λ x10 .
λ x11 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x12 :
(
ι → ι
)
→
ι → ι
.
λ x13 .
x12
(
λ x14 .
x2
(
λ x15 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x16 .
0
)
0
(
λ x15 :
ι →
ι → ι
.
λ x16 x17 .
0
)
)
(
setsum
0
0
)
)
0
)
0
)
(
Inj0
0
)
(
Inj1
0
)
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
ι → ι
.
x3
(
λ x9 x10 .
x7
(
setsum
(
Inj1
0
)
(
Inj1
(
x1
(
λ x11 x12 .
0
)
(
λ x11 .
0
)
(
λ x11 .
0
)
(
λ x11 x12 .
0
)
0
0
)
)
)
)
0
(
x2
(
λ x9 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 .
x9
(
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 .
x1
(
λ x13 x14 .
setsum
0
0
)
(
λ x13 .
0
)
(
λ x13 .
setsum
0
0
)
(
λ x13 x14 .
0
)
0
(
x2
(
λ x13 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x14 .
0
)
0
(
λ x13 :
ι →
ι → ι
.
λ x14 x15 .
0
)
)
)
(
λ x11 :
ι → ι
.
0
)
)
(
x2
(
λ x9 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 .
Inj1
(
x9
(
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 .
0
)
(
λ x11 :
ι → ι
.
0
)
)
)
0
(
λ x9 :
ι →
ι → ι
.
λ x10 x11 .
0
)
)
(
λ x9 :
ι →
ι → ι
.
λ x10 x11 .
x11
)
)
(
Inj1
(
x3
(
λ x9 x10 .
x0
(
λ x11 .
λ x12 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x13 :
(
ι → ι
)
→
ι → ι
.
λ x14 .
setsum
0
0
)
x6
)
(
Inj0
(
x7
0
)
)
(
x3
(
λ x9 x10 .
x10
)
(
Inj1
0
)
x4
(
setsum
0
0
)
)
(
x3
(
λ x9 x10 .
x3
(
λ x11 x12 .
0
)
0
0
0
)
(
setsum
0
0
)
(
x3
(
λ x9 x10 .
0
)
0
0
0
)
(
x0
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 .
0
)
0
)
)
)
)
=
setsum
(
x0
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 .
x9
)
(
Inj0
(
setsum
(
Inj0
0
)
0
)
)
)
0
)
⟶
(
∀ x4 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
∀ x5 .
∀ x6 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
∀ x7 .
x2
(
λ x9 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 .
Inj0
0
)
0
(
λ x9 :
ι →
ι → ι
.
λ x10 x11 .
x0
(
λ x12 .
λ x13 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x14 :
(
ι → ι
)
→
ι → ι
.
λ x15 .
x12
)
x7
)
=
setsum
x7
(
setsum
(
Inj0
(
Inj1
(
Inj0
0
)
)
)
(
x3
(
λ x9 x10 .
Inj0
(
x2
(
λ x11 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x12 .
0
)
0
(
λ x11 :
ι →
ι → ι
.
λ x12 x13 .
0
)
)
)
0
x7
0
)
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x6 .
∀ x7 :
ι → ι
.
x2
(
λ x9 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 .
setsum
0
(
x2
(
λ x11 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x12 .
x12
)
(
x3
(
λ x11 x12 .
0
)
(
Inj1
0
)
(
setsum
0
0
)
x10
)
(
λ x11 :
ι →
ι → ι
.
λ x12 x13 .
x13
)
)
)
(
x3
(
λ x9 x10 .
x1
(
λ x11 x12 .
0
)
(
λ x11 .
x10
)
(
λ x11 .
0
)
(
λ x11 x12 .
0
)
0
(
setsum
0
0
)
)
(
x2
(
λ x9 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 .
x6
)
(
Inj1
x6
)
(
λ x9 :
ι →
ι → ι
.
λ x10 x11 .
setsum
x10
(
x3
(
λ x12 x13 .
0
)
0
0
0
)
)
)
(
setsum
0
(
x0
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 .
0
)
0
)
)
x4
)
(
λ x9 :
ι →
ι → ι
.
λ x10 x11 .
x7
(
x3
(
λ x12 x13 .
setsum
0
0
)
(
x2
(
λ x12 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x13 .
x0
(
λ x14 .
λ x15 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x16 :
(
ι → ι
)
→
ι → ι
.
λ x17 .
0
)
0
)
0
(
λ x12 :
ι →
ι → ι
.
λ x13 x14 .
x3
(
λ x15 x16 .
0
)
0
0
0
)
)
(
setsum
(
x7
0
)
0
)
0
)
)
=
x3
(
λ x9 x10 .
x2
(
λ x11 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x12 .
Inj1
x10
)
(
Inj0
0
)
(
λ x11 :
ι →
ι → ι
.
λ x12 x13 .
0
)
)
(
x7
(
x7
(
x7
x6
)
)
)
(
Inj0
(
x7
0
)
)
(
x7
(
Inj0
(
setsum
(
x1
(
λ x9 x10 .
0
)
(
λ x9 .
0
)
(
λ x9 .
0
)
(
λ x9 x10 .
0
)
0
0
)
(
x1
(
λ x9 x10 .
0
)
(
λ x9 .
0
)
(
λ x9 .
0
)
(
λ x9 x10 .
0
)
0
0
)
)
)
)
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
(
ι →
ι → ι
)
→ ι
.
x1
(
λ x9 x10 .
x6
)
(
λ x9 .
Inj1
0
)
(
λ x9 .
0
)
(
λ x9 x10 .
x9
)
(
Inj0
0
)
(
setsum
(
x3
(
λ x9 x10 .
0
)
(
x3
(
λ x9 x10 .
0
)
(
x7
(
λ x9 x10 .
0
)
)
(
setsum
0
0
)
(
Inj1
0
)
)
(
setsum
(
setsum
0
0
)
x4
)
0
)
0
)
=
setsum
0
x6
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
ι → ι
.
x1
(
λ x9 x10 .
x6
)
(
λ x9 .
x1
(
λ x10 x11 .
0
)
(
λ x10 .
x1
(
λ x11 x12 .
Inj1
x9
)
(
λ x11 .
setsum
(
x1
(
λ x12 x13 .
0
)
(
λ x12 .
0
)
(
λ x12 .
0
)
(
λ x12 x13 .
0
)
0
0
)
(
x2
(
λ x12 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x13 .
0
)
0
(
λ x12 :
ι →
ι → ι
.
λ x13 x14 .
0
)
)
)
(
λ x11 .
x11
)
(
λ x11 x12 .
setsum
0
0
)
0
0
)
(
setsum
x6
)
(
λ x10 x11 .
0
)
x6
(
Inj1
0
)
)
(
λ x9 .
x3
(
λ x10 x11 .
Inj1
x10
)
0
(
x0
(
λ x10 .
λ x11 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x12 :
(
ι → ι
)
→
ι → ι
.
λ x13 .
x12
(
λ x14 .
0
)
x10
)
x6
)
x6
)
(
λ x9 x10 .
0
)
0
(
Inj0
(
x3
(
λ x9 x10 .
x0
(
λ x11 .
λ x12 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x13 :
(
ι → ι
)
→
ι → ι
.
λ x14 .
0
)
0
)
(
Inj0
(
x3
(
λ x9 x10 .
0
)
0
0
0
)
)
0
0
)
)
=
x3
(
λ x9 x10 .
Inj0
0
)
(
setsum
0
0
)
(
x7
x4
)
(
x7
(
x0
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 .
x10
(
λ x13 :
ι → ι
.
0
)
)
(
Inj1
(
Inj0
0
)
)
)
)
)
⟶
(
∀ x4 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x5 x6 x7 .
x0
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 .
setsum
(
x2
(
λ x13 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x14 .
x11
(
λ x15 .
x12
)
x12
)
(
setsum
(
x0
(
λ x13 .
λ x14 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x15 :
(
ι → ι
)
→
ι → ι
.
λ x16 .
0
)
0
)
(
x2
(
λ x13 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x14 .
0
)
0
(
λ x13 :
ι →
ι → ι
.
λ x14 x15 .
0
)
)
)
(
λ x13 :
ι →
ι → ι
.
λ x14 x15 .
0
)
)
0
)
0
=
x4
0
(
λ x9 :
ι → ι
.
setsum
(
x2
(
λ x10 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 .
x10
(
λ x12 :
(
ι → ι
)
→ ι
.
λ x13 .
0
)
(
λ x12 :
ι → ι
.
x2
(
λ x13 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x14 .
0
)
0
(
λ x13 :
ι →
ι → ι
.
λ x14 x15 .
0
)
)
)
0
(
λ x10 :
ι →
ι → ι
.
λ x11 x12 .
0
)
)
(
x1
(
λ x10 x11 .
0
)
(
λ x10 .
x7
)
(
λ x10 .
0
)
(
λ x10 x11 .
0
)
(
x3
(
λ x10 x11 .
setsum
0
0
)
0
x7
x5
)
(
Inj1
(
x2
(
λ x10 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 .
0
)
0
(
λ x10 :
ι →
ι → ι
.
λ x11 x12 .
0
)
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
ι → ι
.
∀ x6 :
ι →
(
ι →
ι → ι
)
→ ι
.
∀ x7 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
x0
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 .
x2
(
λ x13 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x14 .
x0
(
λ x15 .
λ x16 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x17 :
(
ι → ι
)
→
ι → ι
.
λ x18 .
0
)
0
)
0
(
λ x13 :
ι →
ι → ι
.
λ x14 x15 .
0
)
)
(
x0
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 .
x3
(
λ x13 x14 .
0
)
0
(
Inj0
0
)
(
x1
(
λ x13 x14 .
0
)
(
λ x13 .
setsum
0
0
)
(
λ x13 .
x11
(
λ x14 .
0
)
0
)
(
λ x13 x14 .
0
)
0
(
x10
(
λ x13 :
ι → ι
.
0
)
)
)
)
0
)
=
x0
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 .
setsum
(
x2
(
λ x13 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x14 .
Inj1
(
x2
(
λ x15 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x16 .
0
)
0
(
λ x15 :
ι →
ι → ι
.
λ x16 x17 .
0
)
)
)
(
x1
(
λ x13 x14 .
x3
(
λ x15 x16 .
0
)
0
0
0
)
(
λ x13 .
Inj0
0
)
(
λ x13 .
x12
)
(
λ x13 x14 .
Inj0
0
)
(
x10
(
λ x13 :
ι → ι
.
0
)
)
(
Inj1
0
)
)
(
λ x13 :
ι →
ι → ι
.
λ x14 x15 .
setsum
0
0
)
)
x9
)
(
Inj1
(
Inj1
(
x7
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x9 :
ι → ι
.
Inj0
0
)
)
)
)
)
⟶
False
(proof)
Theorem
aeb5f..
:
∀ x0 :
(
(
ι →
ι →
(
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
)
→
(
ι →
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι → ι
.
∀ x1 :
(
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
)
→
(
(
(
ι →
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι →
ι → ι
)
→
ι →
(
ι →
ι → ι
)
→ ι
.
∀ x2 :
(
(
(
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x3 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
(
∀ x4 :
ι → ι
.
∀ x5 .
∀ x6 :
ι → ι
.
∀ x7 .
x3
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
x9
(
λ x10 .
x2
(
λ x11 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
x3
(
λ x12 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x12 .
x0
(
λ x13 :
ι →
ι →
(
ι → ι
)
→ ι
.
λ x14 :
(
ι → ι
)
→
ι → ι
.
λ x15 .
λ x16 :
ι → ι
.
λ x17 .
0
)
(
λ x13 .
λ x14 :
(
ι → ι
)
→ ι
.
0
)
0
)
(
λ x12 :
(
ι → ι
)
→ ι
.
λ x13 :
ι → ι
.
x11
(
λ x14 :
ι → ι
.
λ x15 .
0
)
0
(
λ x14 .
0
)
0
)
)
(
Inj1
(
Inj1
0
)
)
(
λ x11 :
ι → ι
.
0
)
)
0
)
(
λ x9 .
Inj1
x5
)
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
x3
(
λ x11 :
(
ι → ι
)
→
ι → ι
.
x1
(
λ x12 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
setsum
(
x1
(
λ x13 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
(
λ x13 :
(
ι →
ι → ι
)
→ ι
.
λ x14 :
ι → ι
.
λ x15 x16 .
0
)
0
(
λ x13 x14 .
0
)
)
(
x1
(
λ x13 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
(
λ x13 :
(
ι →
ι → ι
)
→ ι
.
λ x14 :
ι → ι
.
λ x15 x16 .
0
)
0
(
λ x13 x14 .
0
)
)
)
(
λ x12 :
(
ι →
ι → ι
)
→ ι
.
λ x13 :
ι → ι
.
λ x14 x15 .
setsum
0
0
)
(
x9
(
λ x12 .
setsum
0
0
)
)
(
λ x12 x13 .
x11
(
λ x14 .
x0
(
λ x15 :
ι →
ι →
(
ι → ι
)
→ ι
.
λ x16 :
(
ι → ι
)
→
ι → ι
.
λ x17 .
λ x18 :
ι → ι
.
λ x19 .
0
)
(
λ x15 .
λ x16 :
(
ι → ι
)
→ ι
.
0
)
0
)
(
x11
(
λ x14 .
0
)
0
)
)
)
(
λ x11 .
x11
)
(
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 :
ι → ι
.
x3
(
λ x13 :
(
ι → ι
)
→
ι → ι
.
x10
0
)
(
λ x13 .
x11
(
λ x14 .
Inj0
0
)
)
(
λ x13 :
(
ι → ι
)
→ ι
.
λ x14 :
ι → ι
.
Inj1
(
x11
(
λ x15 .
0
)
)
)
)
)
=
x3
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
x9
(
λ x10 .
x7
)
(
setsum
(
x0
(
λ x10 :
ι →
ι →
(
ι → ι
)
→ ι
.
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 .
λ x13 :
ι → ι
.
λ x14 .
Inj1
0
)
(
λ x10 .
λ x11 :
(
ι → ι
)
→ ι
.
Inj0
0
)
(
x1
(
λ x10 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
(
λ x10 :
(
ι →
ι → ι
)
→ ι
.
λ x11 :
ι → ι
.
λ x12 x13 .
0
)
0
(
λ x10 x11 .
0
)
)
)
(
x1
(
λ x10 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
x3
(
λ x11 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x11 .
0
)
(
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 :
ι → ι
.
0
)
)
(
λ x10 :
(
ι →
ι → ι
)
→ ι
.
λ x11 :
ι → ι
.
λ x12 x13 .
x10
(
λ x14 x15 .
0
)
)
x7
(
λ x10 x11 .
x3
(
λ x12 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x12 .
0
)
(
λ x12 :
(
ι → ι
)
→ ι
.
λ x13 :
ι → ι
.
0
)
)
)
)
)
(
λ x9 .
Inj0
(
x3
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
x3
(
λ x11 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x11 .
0
)
(
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 :
ι → ι
.
x0
(
λ x13 :
ι →
ι →
(
ι → ι
)
→ ι
.
λ x14 :
(
ι → ι
)
→
ι → ι
.
λ x15 .
λ x16 :
ι → ι
.
λ x17 .
0
)
(
λ x13 .
λ x14 :
(
ι → ι
)
→ ι
.
0
)
0
)
)
(
λ x10 .
Inj1
0
)
(
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 :
ι → ι
.
x3
(
λ x12 :
(
ι → ι
)
→
ι → ι
.
setsum
0
0
)
(
λ x12 .
x2
(
λ x13 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
0
)
0
(
λ x13 :
ι → ι
.
0
)
)
(
λ x12 :
(
ι → ι
)
→ ι
.
λ x13 :
ι → ι
.
setsum
0
0
)
)
)
)
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
x6
(
x6
x7
)
)
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
x3
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
x1
(
λ x10 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
x9
(
λ x11 .
Inj1
(
Inj1
0
)
)
(
x3
(
λ x11 :
(
ι → ι
)
→
ι → ι
.
x3
(
λ x12 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x12 .
0
)
(
λ x12 :
(
ι → ι
)
→ ι
.
λ x13 :
ι → ι
.
0
)
)
(
λ x11 .
x9
(
λ x12 .
0
)
0
)
(
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 :
ι → ι
.
Inj0
0
)
)
)
(
λ x10 :
(
ι →
ι → ι
)
→ ι
.
λ x11 :
ι → ι
.
λ x12 x13 .
0
)
0
(
λ x10 x11 .
0
)
)
(
λ x9 .
x3
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
setsum
x9
(
setsum
0
0
)
)
(
λ x10 .
0
)
(
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 :
ι → ι
.
0
)
)
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
0
)
=
Inj1
0
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
(
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
x2
(
λ x9 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
x0
(
λ x10 :
ι →
ι →
(
ι → ι
)
→ ι
.
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 .
λ x13 :
ι → ι
.
λ x14 .
x11
(
λ x15 .
x2
(
λ x16 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
Inj1
0
)
(
Inj0
0
)
(
λ x16 :
ι → ι
.
x1
(
λ x17 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
(
λ x17 :
(
ι →
ι → ι
)
→ ι
.
λ x18 :
ι → ι
.
λ x19 x20 .
0
)
0
(
λ x17 x18 .
0
)
)
)
(
x2
(
λ x15 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
x12
)
0
(
λ x15 :
ι → ι
.
x3
(
λ x16 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x16 .
0
)
(
λ x16 :
(
ι → ι
)
→ ι
.
λ x17 :
ι → ι
.
0
)
)
)
)
(
λ x10 .
λ x11 :
(
ι → ι
)
→ ι
.
x7
(
λ x12 :
(
ι → ι
)
→
ι → ι
.
λ x13 .
x10
)
(
λ x12 .
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
0
)
(
x0
(
λ x9 :
ι →
ι →
(
ι → ι
)
→ ι
.
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 .
λ x12 :
ι → ι
.
λ x13 .
setsum
x11
(
setsum
x11
0
)
)
(
λ x9 .
λ x10 :
(
ι → ι
)
→ ι
.
x2
(
λ x11 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
Inj0
(
x2
(
λ x12 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
0
)
0
(
λ x12 :
ι → ι
.
0
)
)
)
0
(
λ x11 :
ι → ι
.
x1
(
λ x12 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
setsum
0
0
)
(
λ x12 :
(
ι →
ι → ι
)
→ ι
.
λ x13 :
ι → ι
.
λ x14 x15 .
setsum
0
0
)
(
x0
(
λ x12 :
ι →
ι →
(
ι → ι
)
→ ι
.
λ x13 :
(
ι → ι
)
→
ι → ι
.
λ x14 .
λ x15 :
ι → ι
.
λ x16 .
0
)
(
λ x12 .
λ x13 :
(
ι → ι
)
→ ι
.
0
)
0
)
(
λ x12 x13 .
x12
)
)
)
x6
)
(
λ x9 :
ι → ι
.
Inj0
(
x1
(
λ x10 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
x7
(
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 .
Inj0
0
)
(
λ x11 .
x7
(
λ x12 :
(
ι → ι
)
→
ι → ι
.
λ x13 .
0
)
(
λ x12 .
0
)
)
)
(
λ x10 :
(
ι →
ι → ι
)
→ ι
.
λ x11 :
ι → ι
.
λ x12 x13 .
setsum
(
setsum
0
0
)
0
)
x6
(
λ x10 x11 .
0
)
)
)
=
Inj0
x5
)
⟶
(
∀ x4 :
(
ι → ι
)
→ ι
.
∀ x5 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
∀ x6 x7 .
x2
(
λ x9 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
Inj1
0
)
x7
(
λ x9 :
ι → ι
.
Inj0
0
)
=
x7
)
⟶
(
∀ x4 :
ι →
(
ι → ι
)
→ ι
.
∀ x5 x6 :
ι → ι
.
∀ x7 .
x1
(
λ x9 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
x2
(
λ x10 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
x3
(
λ x11 :
(
ι → ι
)
→
ι → ι
.
x10
(
λ x12 :
ι → ι
.
λ x13 .
0
)
x7
(
λ x12 .
x3
(
λ x13 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x13 .
0
)
(
λ x13 :
(
ι → ι
)
→ ι
.
λ x14 :
ι → ι
.
0
)
)
0
)
(
λ x11 .
Inj1
(
x3
(
λ x12 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x12 .
0
)
(
λ x12 :
(
ι → ι
)
→ ι
.
λ x13 :
ι → ι
.
0
)
)
)
(
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 :
ι → ι
.
x11
(
λ x13 .
x13
)
)
)
0
(
λ x10 :
ι → ι
.
x2
(
λ x11 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
Inj0
x7
)
(
x0
(
λ x11 :
ι →
ι →
(
ι → ι
)
→ ι
.
λ x12 :
(
ι → ι
)
→
ι → ι
.
λ x13 .
λ x14 :
ι → ι
.
λ x15 .
x3
(
λ x16 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x16 .
0
)
(
λ x16 :
(
ι → ι
)
→ ι
.
λ x17 :
ι → ι
.
0
)
)
(
λ x11 .
λ x12 :
(
ι → ι
)
→ ι
.
0
)
0
)
(
λ x11 :
ι → ι
.
x11
(
x3
(
λ x12 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x12 .
0
)
(
λ x12 :
(
ι → ι
)
→ ι
.
λ x13 :
ι → ι
.
0
)
)
)
)
)
(
λ x9 :
(
ι →
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
λ x11 x12 .
x9
(
λ x13 x14 .
0
)
)
0
(
λ x9 x10 .
x2
(
λ x11 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
x2
(
λ x12 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
x0
(
λ x13 :
ι →
ι →
(
ι → ι
)
→ ι
.
λ x14 :
(
ι → ι
)
→
ι → ι
.
λ x15 .
λ x16 :
ι → ι
.
λ x17 .
0
)
(
λ x13 .
λ x14 :
(
ι → ι
)
→ ι
.
0
)
x9
)
x9
(
λ x12 :
ι → ι
.
x2
(
λ x13 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
x3
(
λ x14 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x14 .
0
)
(
λ x14 :
(
ι → ι
)
→ ι
.
λ x15 :
ι → ι
.
0
)
)
(
Inj1
0
)
(
λ x13 :
ι → ι
.
0
)
)
)
0
(
λ x11 :
ι → ι
.
x0
(
λ x12 :
ι →
ι →
(
ι → ι
)
→ ι
.
λ x13 :
(
ι → ι
)
→
ι → ι
.
λ x14 .
λ x15 :
ι → ι
.
λ x16 .
x16
)
(
λ x12 .
λ x13 :
(
ι → ι
)
→ ι
.
x2
(
λ x14 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
x3
(
λ x15 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x15 .
0
)
(
λ x15 :
(
ι → ι
)
→ ι
.
λ x16 :
ι → ι
.
0
)
)
(
Inj1
0
)
(
λ x14 :
ι → ι
.
x0
(
λ x15 :
ι →
ι →
(
ι → ι
)
→ ι
.
λ x16 :
(
ι → ι
)
→
ι → ι
.
λ x17 .
λ x18 :
ι → ι
.
λ x19 .
0
)
(
λ x15 .
λ x16 :
(
ι → ι
)
→ ι
.
0
)
0
)
)
(
x3
(
λ x12 :
(
ι → ι
)
→
ι → ι
.
x1
(
λ x13 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
(
λ x13 :
(
ι →
ι → ι
)
→ ι
.
λ x14 :
ι → ι
.
λ x15 x16 .
0
)
0
(
λ x13 x14 .
0
)
)
(
λ x12 .
0
)
(
λ x12 :
(
ι → ι
)
→ ι
.
λ x13 :
ι → ι
.
x3
(
λ x14 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x14 .
0
)
(
λ x14 :
(
ι → ι
)
→ ι
.
λ x15 :
ι → ι
.
0
)
)
)
)
)
=
x2
(
λ x9 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
Inj0
(
x6
0
)
)
(
Inj0
(
setsum
(
x1
(
λ x9 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
Inj1
0
)
(
λ x9 :
(
ι →
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
λ x11 x12 .
setsum
0
0
)
(
setsum
0
0
)
(
λ x9 x10 .
0
)
)
(
x1
(
λ x9 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
setsum
0
0
)
(
λ x9 :
(
ι →
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
λ x11 x12 .
x12
)
(
setsum
0
0
)
(
λ x9 x10 .
x10
)
)
)
)
(
λ x9 :
ι → ι
.
x9
0
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x5 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x6 .
∀ x7 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→ ι
.
x1
(
λ x9 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
x9
(
λ x10 :
ι → ι
.
λ x11 .
setsum
(
setsum
x11
(
x0
(
λ x12 :
ι →
ι →
(
ι → ι
)
→ ι
.
λ x13 :
(
ι → ι
)
→
ι → ι
.
λ x14 .
λ x15 :
ι → ι
.
λ x16 .
0
)
(
λ x12 .
λ x13 :
(
ι → ι
)
→ ι
.
0
)
0
)
)
(
x3
(
λ x12 :
(
ι → ι
)
→
ι → ι
.
x3
(
λ x13 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x13 .
0
)
(
λ x13 :
(
ι → ι
)
→ ι
.
λ x14 :
ι → ι
.
0
)
)
(
λ x12 .
Inj1
0
)
(
λ x12 :
(
ι → ι
)
→ ι
.
λ x13 :
ι → ι
.
0
)
)
)
)
(
λ x9 :
(
ι →
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
λ x11 x12 .
x3
(
λ x13 :
(
ι → ι
)
→
ι → ι
.
x0
(
λ x14 :
ι →
ι →
(
ι → ι
)
→ ι
.
λ x15 :
(
ι → ι
)
→
ι → ι
.
λ x16 .
λ x17 :
ι → ι
.
λ x18 .
Inj1
(
setsum
0
0
)
)
(
λ x14 .
λ x15 :
(
ι → ι
)
→ ι
.
setsum
(
x13
(
λ x16 .
0
)
0
)
(
x2
(
λ x16 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
0
)
0
(
λ x16 :
ι → ι
.
0
)
)
)
(
x0
(
λ x14 :
ι →
ι →
(
ι → ι
)
→ ι
.
λ x15 :
(
ι → ι
)
→
ι → ι
.
λ x16 .
λ x17 :
ι → ι
.
λ x18 .
0
)
(
λ x14 .
λ x15 :
(
ι → ι
)
→ ι
.
x13
(
λ x16 .
0
)
0
)
(
x13
(
λ x14 .
0
)
0
)
)
)
(
λ x13 .
Inj0
x12
)
(
λ x13 :
(
ι → ι
)
→ ι
.
λ x14 :
ι → ι
.
x12
)
)
(
Inj1
(
x0
(
λ x9 :
ι →
ι →
(
ι → ι
)
→ ι
.
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 .
λ x12 :
ι → ι
.
λ x13 .
Inj0
0
)
(
λ x9 .
λ x10 :
(
ι → ι
)
→ ι
.
0
)
(
x7
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 x11 .
x11
)
)
)
)
(
λ x9 x10 .
Inj0
(
Inj0
(
setsum
(
setsum
0
0
)
(
Inj0
0
)
)
)
)
=
x3
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
setsum
(
x5
(
Inj1
(
x3
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x10 .
0
)
(
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 :
ι → ι
.
0
)
)
)
(
λ x10 :
ι → ι
.
0
)
)
(
Inj1
0
)
)
(
λ x9 .
setsum
0
(
x7
(
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 x12 .
0
)
)
)
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
setsum
(
x7
(
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 x13 .
x0
(
λ x14 :
ι →
ι →
(
ι → ι
)
→ ι
.
λ x15 :
(
ι → ι
)
→
ι → ι
.
λ x16 .
λ x17 :
ι → ι
.
λ x18 .
Inj0
0
)
(
λ x14 .
λ x15 :
(
ι → ι
)
→ ι
.
0
)
(
setsum
0
0
)
)
)
(
Inj1
(
x7
(
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 x13 .
Inj0
0
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
(
ι → ι
)
→ ι
.
∀ x6 :
ι →
ι → ι
.
∀ x7 .
x0
(
λ x9 :
ι →
ι →
(
ι → ι
)
→ ι
.
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 .
λ x12 :
ι → ι
.
λ x13 .
Inj0
(
x10
(
λ x14 .
0
)
(
x12
(
x0
(
λ x14 :
ι →
ι →
(
ι → ι
)
→ ι
.
λ x15 :
(
ι → ι
)
→
ι → ι
.
λ x16 .
λ x17 :
ι → ι
.
λ x18 .
0
)
(
λ x14 .
λ x15 :
(
ι → ι
)
→ ι
.
0
)
0
)
)
)
)
(
λ x9 .
λ x10 :
(
ι → ι
)
→ ι
.
x3
(
λ x11 :
(
ι → ι
)
→
ι → ι
.
x9
)
(
λ x11 .
Inj0
0
)
(
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 :
ι → ι
.
x9
)
)
0
=
x3
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
x2
(
λ x10 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
x2
(
λ x11 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
x1
(
λ x12 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
Inj1
0
)
(
λ x12 :
(
ι →
ι → ι
)
→ ι
.
λ x13 :
ι → ι
.
λ x14 x15 .
0
)
(
x0
(
λ x12 :
ι →
ι →
(
ι → ι
)
→ ι
.
λ x13 :
(
ι → ι
)
→
ι → ι
.
λ x14 .
λ x15 :
ι → ι
.
λ x16 .
0
)
(
λ x12 .
λ x13 :
(
ι → ι
)
→ ι
.
0
)
0
)
(
λ x12 x13 .
Inj0
0
)
)
(
x1
(
λ x11 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
(
λ x11 :
(
ι →
ι → ι
)
→ ι
.
λ x12 :
ι → ι
.
λ x13 x14 .
x1
(
λ x15 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
(
λ x15 :
(
ι →
ι → ι
)
→ ι
.
λ x16 :
ι → ι
.
λ x17 x18 .
0
)
0
(
λ x15 x16 .
0
)
)
0
(
λ x11 x12 .
setsum
0
0
)
)
(
λ x11 :
ι → ι
.
x0
(
λ x12 :
ι →
ι →
(
ι → ι
)
→ ι
.
λ x13 :
(
ι → ι
)
→
ι → ι
.
λ x14 .
λ x15 :
ι → ι
.
λ x16 .
x16
)
(
λ x12 .
λ x13 :
(
ι → ι
)
→ ι
.
Inj1
0
)
(
x10
(
λ x12 :
ι → ι
.
λ x13 .
0
)
0
(
λ x12 .
0
)
0
)
)
)
(
x1
(
λ x10 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
x3
(
λ x11 :
(
ι → ι
)
→
ι → ι
.
Inj0
0
)
(
λ x11 .
x9
(
λ x12 .
0
)
0
)
(
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 :
ι → ι
.
x1
(
λ x13 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
(
λ x13 :
(
ι →
ι → ι
)
→ ι
.
λ x14 :
ι → ι
.
λ x15 x16 .
0
)
0
(
λ x13 x14 .
0
)
)
)
(
λ x10 :
(
ι →
ι → ι
)
→ ι
.
λ x11 :
ι → ι
.
λ x12 x13 .
0
)
x7
(
λ x10 x11 .
x2
(
λ x12 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
x12
(
λ x13 :
ι → ι
.
λ x14 .
0
)
0
(
λ x13 .
0
)
0
)
0
(
λ x12 :
ι → ι
.
x0
(
λ x13 :
ι →
ι →
(
ι → ι
)
→ ι
.
λ x14 :
(
ι → ι
)
→
ι → ι
.
λ x15 .
λ x16 :
ι → ι
.
λ x17 .
0
)
(
λ x13 .
λ x14 :
(
ι → ι
)
→ ι
.
0
)
0
)
)
)
(
λ x10 :
ι → ι
.
Inj1
(
Inj1
(
x2
(
λ x11 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
0
)
0
(
λ x11 :
ι → ι
.
0
)
)
)
)
)
(
λ x9 .
Inj0
(
setsum
(
x1
(
λ x10 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
(
λ x10 :
(
ι →
ι → ι
)
→ ι
.
λ x11 :
ι → ι
.
λ x12 x13 .
0
)
0
(
λ x10 x11 .
x2
(
λ x12 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
0
)
0
(
λ x12 :
ι → ι
.
0
)
)
)
(
Inj1
x7
)
)
)
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
x1
(
λ x11 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
(
λ x11 :
(
ι →
ι → ι
)
→ ι
.
λ x12 :
ι → ι
.
λ x13 x14 .
0
)
(
x0
(
λ x11 :
ι →
ι →
(
ι → ι
)
→ ι
.
λ x12 :
(
ι → ι
)
→
ι → ι
.
λ x13 .
λ x14 :
ι → ι
.
λ x15 .
setsum
x15
0
)
(
λ x11 .
λ x12 :
(
ι → ι
)
→ ι
.
x3
(
λ x13 :
(
ι → ι
)
→
ι → ι
.
Inj1
0
)
(
λ x13 .
0
)
(
λ x13 :
(
ι → ι
)
→ ι
.
λ x14 :
ι → ι
.
x0
(
λ x15 :
ι →
ι →
(
ι → ι
)
→ ι
.
λ x16 :
(
ι → ι
)
→
ι → ι
.
λ x17 .
λ x18 :
ι → ι
.
λ x19 .
0
)
(
λ x15 .
λ x16 :
(
ι → ι
)
→ ι
.
0
)
0
)
)
(
x3
(
λ x11 :
(
ι → ι
)
→
ι → ι
.
x0
(
λ x12 :
ι →
ι →
(
ι → ι
)
→ ι
.
λ x13 :
(
ι → ι
)
→
ι → ι
.
λ x14 .
λ x15 :
ι → ι
.
λ x16 .
0
)
(
λ x12 .
λ x13 :
(
ι → ι
)
→ ι
.
0
)
0
)
(
λ x11 .
x2
(
λ x12 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
0
)
0
(
λ x12 :
ι → ι
.
0
)
)
(
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 :
ι → ι
.
0
)
)
)
(
λ x11 x12 .
x12
)
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→
ι → ι
.
∀ x5 :
ι → ι
.
∀ x6 :
ι →
(
ι → ι
)
→
ι →
ι → ι
.
∀ x7 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
.
x0
(
λ x9 :
ι →
ι →
(
ι → ι
)
→ ι
.
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 .
λ x12 :
ι → ι
.
λ x13 .
Inj1
(
x2
(
λ x14 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
x3
(
λ x15 :
(
ι → ι
)
→
ι → ι
.
x3
(
λ x16 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x16 .
0
)
(
λ x16 :
(
ι → ι
)
→ ι
.
λ x17 :
ι → ι
.
0
)
)
(
λ x15 .
setsum
0
0
)
(
λ x15 :
(
ι → ι
)
→ ι
.
λ x16 :
ι → ι
.
0
)
)
x11
(
λ x14 :
ι → ι
.
0
)
)
)
(
λ x9 .
λ x10 :
(
ι → ι
)
→ ι
.
0
)
0
=
x5
(
x0
(
λ x9 :
ι →
ι →
(
ι → ι
)
→ ι
.
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 .
λ x12 :
ι → ι
.
λ x13 .
0
)
(
λ x9 .
λ x10 :
(
ι → ι
)
→ ι
.
setsum
(
x10
(
λ x11 .
x9
)
)
0
)
(
setsum
(
x3
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
x6
0
(
λ x10 .
0
)
0
0
)
(
λ x9 .
x1
(
λ x10 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
(
λ x10 :
(
ι →
ι → ι
)
→ ι
.
λ x11 :
ι → ι
.
λ x12 x13 .
0
)
0
(
λ x10 x11 .
0
)
)
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
0
)
)
(
Inj1
(
x3
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x9 .
0
)
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
0
)
)
)
)
)
)
⟶
False
(proof)
Theorem
c1b22..
:
∀ x0 :
(
ι → ι
)
→
ι →
(
(
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
∀ x1 :
(
(
ι → ι
)
→
ι →
ι → ι
)
→
ι →
(
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
∀ x2 :
(
ι →
ι →
ι →
ι → ι
)
→
ι →
(
(
ι →
ι → ι
)
→ ι
)
→ ι
.
∀ x3 :
(
(
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι → ι
.
(
∀ x4 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
∀ x5 .
∀ x6 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x7 .
x3
(
λ x9 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
0
)
0
=
x6
(
setsum
(
setsum
(
setsum
x5
0
)
0
)
(
Inj0
(
x3
(
λ x9 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
x3
(
λ x10 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
0
)
0
)
0
)
)
)
(
λ x9 :
ι → ι
.
Inj0
(
x9
0
)
)
)
⟶
(
∀ x4 .
∀ x5 :
(
ι → ι
)
→ ι
.
∀ x6 x7 .
x3
(
λ x9 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
x0
(
λ x10 .
Inj0
x6
)
(
x5
(
λ x10 .
x3
(
λ x11 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
x0
(
λ x12 .
0
)
0
(
λ x12 :
ι → ι
.
0
)
(
λ x12 :
ι → ι
.
λ x13 .
0
)
0
0
)
(
x9
(
λ x11 .
0
)
(
λ x11 :
ι → ι
.
λ x12 .
0
)
0
)
)
)
(
λ x10 :
ι → ι
.
0
)
(
λ x10 :
ι → ι
.
λ x11 .
x9
(
λ x12 .
Inj1
0
)
(
λ x12 :
ι → ι
.
λ x13 .
x1
(
λ x14 :
ι → ι
.
λ x15 x16 .
x14
0
)
(
Inj1
0
)
(
λ x14 x15 :
ι → ι
.
λ x16 .
0
)
(
setsum
0
0
)
)
(
Inj0
(
setsum
0
0
)
)
)
x6
(
Inj1
(
x9
(
λ x10 .
x2
(
λ x11 x12 x13 x14 .
0
)
0
(
λ x11 :
ι →
ι → ι
.
0
)
)
(
λ x10 :
ι → ι
.
λ x11 .
x3
(
λ x12 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
0
)
0
)
0
)
)
)
0
=
x0
(
λ x9 .
Inj0
(
x1
(
λ x10 :
ι → ι
.
λ x11 x12 .
0
)
(
x2
(
λ x10 x11 x12 x13 .
x11
)
0
(
λ x10 :
ι →
ι → ι
.
x2
(
λ x11 x12 x13 x14 .
0
)
0
(
λ x11 :
ι →
ι → ι
.
0
)
)
)
(
λ x10 x11 :
ι → ι
.
λ x12 .
0
)
(
Inj1
(
setsum
0
0
)
)
)
)
x4
(
λ x9 :
ι → ι
.
setsum
0
0
)
(
λ x9 :
ι → ι
.
λ x10 .
x1
(
λ x11 :
ι → ι
.
λ x12 x13 .
x1
(
λ x14 :
ι → ι
.
λ x15 x16 .
x16
)
(
Inj0
0
)
(
λ x14 x15 :
ι → ι
.
λ x16 .
setsum
x16
0
)
(
setsum
(
x11
0
)
(
x3
(
λ x14 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
0
)
0
)
)
)
(
x2
(
λ x11 x12 x13 x14 .
x0
(
λ x15 .
x15
)
0
(
λ x15 :
ι → ι
.
Inj1
0
)
(
λ x15 :
ι → ι
.
λ x16 .
x16
)
x14
(
x3
(
λ x15 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
0
)
0
)
)
(
setsum
x10
(
x1
(
λ x11 :
ι → ι
.
λ x12 x13 .
0
)
0
(
λ x11 x12 :
ι → ι
.
λ x13 .
0
)
0
)
)
(
λ x11 :
ι →
ι → ι
.
0
)
)
(
λ x11 x12 :
ι → ι
.
x12
)
(
Inj1
(
x9
0
)
)
)
(
Inj1
(
x0
(
λ x9 .
setsum
(
x3
(
λ x10 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
0
)
0
)
(
x2
(
λ x10 x11 x12 x13 .
0
)
0
(
λ x10 :
ι →
ι → ι
.
0
)
)
)
(
x0
(
λ x9 .
Inj1
0
)
0
(
λ x9 :
ι → ι
.
x7
)
(
λ x9 :
ι → ι
.
λ x10 .
0
)
(
setsum
0
0
)
(
x5
(
λ x9 .
0
)
)
)
(
λ x9 :
ι → ι
.
Inj1
(
Inj0
0
)
)
(
λ x9 :
ι → ι
.
λ x10 .
0
)
(
Inj0
x4
)
0
)
)
(
x1
(
λ x9 :
ι → ι
.
λ x10 x11 .
x7
)
0
(
λ x9 x10 :
ι → ι
.
λ x11 .
0
)
(
x5
(
λ x9 .
x1
(
λ x10 :
ι → ι
.
λ x11 x12 .
x0
(
λ x13 .
0
)
0
(
λ x13 :
ι → ι
.
0
)
(
λ x13 :
ι → ι
.
λ x14 .
0
)
0
0
)
0
(
λ x10 x11 :
ι → ι
.
λ x12 .
Inj1
0
)
(
Inj0
0
)
)
)
)
)
⟶
(
∀ x4 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
∀ x5 .
∀ x6 :
(
ι → ι
)
→
ι →
(
ι → ι
)
→ ι
.
∀ x7 :
ι →
(
ι → ι
)
→ ι
.
x2
(
λ x9 x10 x11 x12 .
0
)
(
x3
(
λ x9 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
x5
)
x5
)
(
λ x9 :
ι →
ι → ι
.
Inj1
(
x2
(
λ x10 x11 x12 x13 .
Inj1
x12
)
(
x3
(
λ x10 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
x6
(
λ x11 .
0
)
0
(
λ x11 .
0
)
)
(
setsum
0
0
)
)
(
λ x10 :
ι →
ι → ι
.
0
)
)
)
=
Inj0
0
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
ι →
ι →
(
ι → ι
)
→ ι
.
x2
(
λ x9 x10 x11 x12 .
0
)
(
setsum
(
setsum
(
x2
(
λ x9 x10 x11 x12 .
x3
(
λ x13 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
0
)
0
)
0
(
λ x9 :
ι →
ι → ι
.
0
)
)
(
x0
(
λ x9 .
0
)
(
Inj1
0
)
(
λ x9 :
ι → ι
.
0
)
(
λ x9 :
ι → ι
.
λ x10 .
setsum
0
0
)
(
setsum
0
0
)
(
x0
(
λ x9 .
0
)
0
(
λ x9 :
ι → ι
.
0
)
(
λ x9 :
ι → ι
.
λ x10 .
0
)
0
0
)
)
)
(
x1
(
λ x9 :
ι → ι
.
λ x10 x11 .
Inj1
(
x7
0
0
(
λ x12 .
0
)
)
)
(
x0
(
λ x9 .
x9
)
x4
(
λ x9 :
ι → ι
.
setsum
0
0
)
(
λ x9 :
ι → ι
.
λ x10 .
Inj0
0
)
(
Inj1
0
)
x4
)
(
λ x9 x10 :
ι → ι
.
λ x11 .
0
)
x4
)
)
(
λ x9 :
ι →
ι → ι
.
0
)
=
setsum
(
x3
(
λ x9 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
0
)
(
x0
(
λ x9 .
x7
(
setsum
0
0
)
(
setsum
0
0
)
(
λ x10 .
setsum
0
0
)
)
x5
(
λ x9 :
ι → ι
.
x5
)
(
λ x9 :
ι → ι
.
λ x10 .
0
)
(
x1
(
λ x9 :
ι → ι
.
λ x10 x11 .
setsum
0
0
)
(
Inj1
0
)
(
λ x9 x10 :
ι → ι
.
λ x11 .
Inj1
0
)
0
)
(
Inj1
x6
)
)
)
0
)
⟶
(
∀ x4 .
∀ x5 :
ι →
ι → ι
.
∀ x6 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x7 .
x1
(
λ x9 :
ι → ι
.
λ x10 x11 .
x10
)
x7
(
λ x9 x10 :
ι → ι
.
λ x11 .
setsum
0
0
)
0
=
x7
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
.
∀ x5 :
ι →
ι → ι
.
∀ x6 .
∀ x7 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
x1
(
λ x9 :
ι → ι
.
λ x10 x11 .
x1
(
λ x12 :
ι → ι
.
λ x13 x14 .
0
)
0
(
λ x12 x13 :
ι → ι
.
λ x14 .
setsum
(
setsum
x11
(
x2
(
λ x15 x16 x17 x18 .
0
)
0
(
λ x15 :
ι →
ι → ι
.
0
)
)
)
(
x3
(
λ x15 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
0
)
(
x1
(
λ x15 :
ι → ι
.
λ x16 x17 .
0
)
0
(
λ x15 x16 :
ι → ι
.
λ x17 .
0
)
0
)
)
)
x11
)
(
x0
(
setsum
0
)
(
x2
(
λ x9 x10 x11 x12 .
x12
)
(
x1
(
λ x9 :
ι → ι
.
λ x10 x11 .
Inj0
0
)
(
x2
(
λ x9 x10 x11 x12 .
0
)
0
(
λ x9 :
ι →
ι → ι
.
0
)
)
(
λ x9 x10 :
ι → ι
.
λ x11 .
0
)
0
)
(
λ x9 :
ι →
ι → ι
.
x9
x6
(
x1
(
λ x10 :
ι → ι
.
λ x11 x12 .
0
)
0
(
λ x10 x11 :
ι → ι
.
λ x12 .
0
)
0
)
)
)
(
λ x9 :
ι → ι
.
0
)
(
λ x9 :
ι → ι
.
λ x10 .
x0
(
λ x11 .
setsum
(
x2
(
λ x12 x13 x14 x15 .
0
)
0
(
λ x12 :
ι →
ι → ι
.
0
)
)
0
)
(
x0
(
λ x11 .
0
)
0
(
λ x11 :
ι → ι
.
Inj0
0
)
(
λ x11 :
ι → ι
.
λ x12 .
0
)
(
x1
(
λ x11 :
ι → ι
.
λ x12 x13 .
0
)
0
(
λ x11 x12 :
ι → ι
.
λ x13 .
0
)
0
)
(
x9
0
)
)
(
λ x11 :
ι → ι
.
x2
(
λ x12 x13 x14 x15 .
0
)
0
(
λ x12 :
ι →
ι → ι
.
Inj1
0
)
)
(
λ x11 :
ι → ι
.
λ x12 .
0
)
0
(
x3
(
λ x11 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
x11
(
λ x12 .
0
)
(
λ x12 :
ι → ι
.
λ x13 .
0
)
0
)
(
x3
(
λ x11 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
0
)
0
)
)
)
(
setsum
(
Inj0
(
x5
0
0
)
)
(
x0
(
λ x9 .
x5
0
0
)
(
Inj1
0
)
(
λ x9 :
ι → ι
.
0
)
(
λ x9 :
ι → ι
.
λ x10 .
setsum
0
0
)
(
x5
0
0
)
(
x5
0
0
)
)
)
(
x5
(
Inj1
(
x4
(
λ x9 :
(
ι → ι
)
→ ι
.
0
)
)
)
(
x4
(
λ x9 :
(
ι → ι
)
→ ι
.
0
)
)
)
)
(
λ x9 x10 :
ι → ι
.
λ x11 .
x9
0
)
(
Inj0
(
x0
(
λ x9 .
Inj1
(
x0
(
λ x10 .
0
)
0
(
λ x10 :
ι → ι
.
0
)
(
λ x10 :
ι → ι
.
λ x11 .
0
)
0
0
)
)
(
x3
(
λ x9 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
x1
(
λ x10 :
ι → ι
.
λ x11 x12 .
0
)
0
(
λ x10 x11 :
ι → ι
.
λ x12 .
0
)
0
)
(
x1
(
λ x9 :
ι → ι
.
λ x10 x11 .
0
)
0
(
λ x9 x10 :
ι → ι
.
λ x11 .
0
)
0
)
)
(
λ x9 :
ι → ι
.
Inj1
(
x3
(
λ x10 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
0
)
0
)
)
(
λ x9 :
ι → ι
.
λ x10 .
setsum
(
x1
(
λ x11 :
ι → ι
.
λ x12 x13 .
0
)
0
(
λ x11 x12 :
ι → ι
.
λ x13 .
0
)
0
)
(
x9
0
)
)
(
x3
(
λ x9 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
x6
)
x6
)
(
x4
(
λ x9 :
(
ι → ι
)
→ ι
.
x5
0
0
)
)
)
)
=
x0
(
λ x9 .
setsum
x9
0
)
(
x7
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 .
x11
)
(
λ x9 :
ι → ι
.
0
)
(
x5
0
(
setsum
(
x2
(
λ x9 x10 x11 x12 .
0
)
0
(
λ x9 :
ι →
ι → ι
.
0
)
)
(
setsum
0
0
)
)
)
)
(
λ x9 :
ι → ι
.
x3
(
λ x10 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
x0
(
λ x11 .
0
)
(
x2
(
λ x11 x12 x13 x14 .
Inj1
0
)
(
x1
(
λ x11 :
ι → ι
.
λ x12 x13 .
0
)
0
(
λ x11 x12 :
ι → ι
.
λ x13 .
0
)
0
)
(
λ x11 :
ι →
ι → ι
.
x10
(
λ x12 .
0
)
(
λ x12 :
ι → ι
.
λ x13 .
0
)
0
)
)
(
λ x11 :
ι → ι
.
x0
(
λ x12 .
x0
(
λ x13 .
0
)
0
(
λ x13 :
ι → ι
.
0
)
(
λ x13 :
ι → ι
.
λ x14 .
0
)
0
0
)
(
x2
(
λ x12 x13 x14 x15 .
0
)
0
(
λ x12 :
ι →
ι → ι
.
0
)
)
(
λ x12 :
ι → ι
.
x10
(
λ x13 .
0
)
(
λ x13 :
ι → ι
.
λ x14 .
0
)
0
)
(
λ x12 :
ι → ι
.
λ x13 .
Inj0
0
)
(
Inj1
0
)
(
setsum
0
0
)
)
(
λ x11 :
ι → ι
.
λ x12 .
0
)
(
x10
(
λ x11 .
x7
(
λ x12 .
λ x13 :
ι → ι
.
λ x14 .
0
)
(
λ x12 :
ι → ι
.
0
)
0
)
(
λ x11 :
ι → ι
.
λ x12 .
0
)
(
Inj1
0
)
)
(
setsum
0
(
Inj0
0
)
)
)
(
x1
(
λ x10 :
ι → ι
.
λ x11 x12 .
x9
(
Inj0
0
)
)
(
x2
(
λ x10 x11 x12 x13 .
x12
)
(
x3
(
λ x10 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
0
)
0
)
(
λ x10 :
ι →
ι → ι
.
x7
(
λ x11 .
λ x12 :
ι → ι
.
λ x13 .
0
)
(
λ x11 :
ι → ι
.
0
)
0
)
)
(
λ x10 x11 :
ι → ι
.
λ x12 .
setsum
(
x9
0
)
(
setsum
0
0
)
)
(
Inj0
(
x5
0
0
)
)
)
)
(
λ x9 :
ι → ι
.
λ x10 .
setsum
(
x9
(
x0
(
λ x11 .
x11
)
(
x3
(
λ x11 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
0
)
0
)
(
λ x11 :
ι → ι
.
0
)
(
λ x11 :
ι → ι
.
λ x12 .
x1
(
λ x13 :
ι → ι
.
λ x14 x15 .
0
)
0
(
λ x13 x14 :
ι → ι
.
λ x15 .
0
)
0
)
(
x2
(
λ x11 x12 x13 x14 .
0
)
0
(
λ x11 :
ι →
ι → ι
.
0
)
)
(
x9
0
)
)
)
0
)
(
x7
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 .
setsum
0
0
)
(
λ x9 :
ι → ι
.
setsum
0
(
x2
(
λ x10 x11 x12 x13 .
Inj0
0
)
0
(
λ x10 :
ι →
ι → ι
.
x7
(
λ x11 .
λ x12 :
ι → ι
.
λ x13 .
0
)
(
λ x11 :
ι → ι
.
0
)
0
)
)
)
(
x1
(
λ x9 :
ι → ι
.
λ x10 x11 .
x0
(
λ x12 .
x9
0
)
(
x9
0
)
(
λ x12 :
ι → ι
.
x9
0
)
(
λ x12 :
ι → ι
.
λ x13 .
setsum
0
0
)
(
x2
(
λ x12 x13 x14 x15 .
0
)
0
(
λ x12 :
ι →
ι → ι
.
0
)
)
0
)
(
setsum
(
x4
(
λ x9 :
(
ι → ι
)
→ ι
.
0
)
)
0
)
(
λ x9 x10 :
ι → ι
.
λ x11 .
Inj1
0
)
(
x0
(
λ x9 .
0
)
(
x4
(
λ x9 :
(
ι → ι
)
→ ι
.
0
)
)
(
λ x9 :
ι → ι
.
x5
0
0
)
(
λ x9 :
ι → ι
.
λ x10 .
x9
0
)
(
setsum
0
0
)
x6
)
)
)
(
setsum
(
x7
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 .
0
)
(
λ x9 :
ι → ι
.
x3
(
λ x10 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
x0
(
λ x11 .
0
)
0
(
λ x11 :
ι → ι
.
0
)
(
λ x11 :
ι → ι
.
λ x12 .
0
)
0
0
)
(
x5
0
0
)
)
x6
)
(
x4
(
λ x9 :
(
ι → ι
)
→ ι
.
setsum
0
(
x9
(
λ x10 .
0
)
)
)
)
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
ι → ι
.
∀ x7 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
x0
(
λ x9 .
x7
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
x1
(
λ x11 :
ι → ι
.
λ x12 x13 .
x10
(
λ x14 .
x13
)
0
)
(
x7
(
λ x11 :
(
ι → ι
)
→
ι → ι
.
x7
(
λ x12 :
(
ι → ι
)
→
ι → ι
.
0
)
0
(
λ x12 .
0
)
0
)
0
(
λ x11 .
setsum
0
0
)
(
setsum
0
0
)
)
(
λ x11 x12 :
ι → ι
.
λ x13 .
x10
(
λ x14 .
setsum
0
0
)
(
x12
0
)
)
(
setsum
(
x2
(
λ x11 x12 x13 x14 .
0
)
0
(
λ x11 :
ι →
ι → ι
.
0
)
)
(
x1
(
λ x11 :
ι → ι
.
λ x12 x13 .
0
)
0
(
λ x11 x12 :
ι → ι
.
λ x13 .
0
)
0
)
)
)
0
(
λ x10 .
0
)
(
setsum
(
x6
x9
)
0
)
)
(
Inj0
(
setsum
(
x2
(
λ x9 x10 x11 x12 .
x11
)
0
(
λ x9 :
ι →
ι → ι
.
0
)
)
(
x6
(
Inj1
0
)
)
)
)
(
λ x9 :
ι → ι
.
setsum
(
x7
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
0
)
(
x1
(
λ x10 :
ι → ι
.
λ x11 x12 .
setsum
0
0
)
0
(
λ x10 x11 :
ι → ι
.
λ x12 .
setsum
0
0
)
(
x3
(
λ x10 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
0
)
0
)
)
(
λ x10 .
x3
(
λ x11 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
x10
)
(
x1
(
λ x11 :
ι → ι
.
λ x12 x13 .
0
)
0
(
λ x11 x12 :
ι → ι
.
λ x13 .
0
)
0
)
)
0
)
x5
)
(
λ x9 :
ι → ι
.
λ x10 .
0
)
(
x0
(
λ x9 .
x1
(
λ x10 :
ι → ι
.
λ x11 x12 .
x3
(
λ x13 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
x3
(
λ x14 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
0
)
0
)
x9
)
(
setsum
x5
(
x3
(
λ x10 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
0
)
0
)
)
(
λ x10 x11 :
ι → ι
.
λ x12 .
x0
(
λ x13 .
Inj0
0
)
(
setsum
0
0
)
(
λ x13 :
ι → ι
.
0
)
(
λ x13 :
ι → ι
.
λ x14 .
x1
(
λ x15 :
ι → ι
.
λ x16 x17 .
0
)
0
(
λ x15 x16 :
ι → ι
.
λ x17 .
0
)
0
)
0
0
)
x9
)
x4
(
λ x9 :
ι → ι
.
x6
0
)
(
λ x9 :
ι → ι
.
λ x10 .
0
)
(
Inj1
x5
)
0
)
(
x1
(
λ x9 :
ι → ι
.
λ x10 x11 .
Inj0
(
x2
(
λ x12 x13 x14 x15 .
0
)
(
setsum
0
0
)
(
λ x12 :
ι →
ι → ι
.
Inj1
0
)
)
)
0
(
λ x9 x10 :
ι → ι
.
λ x11 .
Inj1
(
x7
(
λ x12 :
(
ι → ι
)
→
ι → ι
.
x12
(
λ x13 .
0
)
0
)
(
x7
(
λ x12 :
(
ι → ι
)
→
ι → ι
.
0
)
0
(
λ x12 .
0
)
0
)
(
λ x12 .
x9
0
)
(
setsum
0
0
)
)
)
0
)
=
setsum
x5
(
Inj0
(
setsum
0
(
x6
(
x7
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
0
)
0
(
λ x9 .
0
)
0
)
)
)
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→ ι
.
∀ x5 :
ι → ι
.
∀ x6 .
∀ x7 :
ι →
ι → ι
.
x0
(
λ x9 .
x1
(
λ x10 :
ι → ι
.
λ x11 x12 .
0
)
(
x2
(
λ x10 x11 x12 x13 .
0
)
(
x5
(
Inj1
0
)
)
(
λ x10 :
ι →
ι → ι
.
x2
(
λ x11 x12 x13 x14 .
setsum
0
0
)
0
(
λ x11 :
ι →
ι → ι
.
x9
)
)
)
(
λ x10 x11 :
ι → ι
.
λ x12 .
setsum
(
Inj1
x9
)
(
setsum
x9
(
setsum
0
0
)
)
)
0
)
(
x7
(
x3
(
λ x9 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
setsum
(
setsum
0
0
)
(
x7
0
0
)
)
(
x4
(
λ x9 .
x5
0
)
)
)
(
x3
(
λ x9 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
x2
(
λ x10 x11 x12 x13 .
Inj1
0
)
(
x2
(
λ x10 x11 x12 x13 .
0
)
0
(
λ x10 :
ι →
ι → ι
.
0
)
)
(
λ x10 :
ι →
ι → ι
.
x9
(
λ x11 .
0
)
(
λ x11 :
ι → ι
.
λ x12 .
0
)
0
)
)
(
x2
(
λ x9 x10 x11 x12 .
0
)
(
setsum
0
0
)
(
λ x9 :
ι →
ι → ι
.
setsum
0
0
)
)
)
)
(
λ x9 :
ι → ι
.
setsum
(
setsum
0
0
)
0
)
(
λ x9 :
ι → ι
.
λ x10 .
0
)
0
x6
=
x1
(
λ x9 :
ι → ι
.
λ x10 x11 .
x7
0
(
x3
(
λ x12 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
x3
(
λ x13 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
Inj1
0
)
(
setsum
0
0
)
)
(
x2
(
λ x12 x13 x14 x15 .
x2
(
λ x16 x17 x18 x19 .
0
)
0
(
λ x16 :
ι →
ι → ι
.
0
)
)
(
setsum
0
0
)
(
λ x12 :
ι →
ι → ι
.
setsum
0
0
)
)
)
)
(
Inj1
(
Inj1
0
)
)
(
λ x9 x10 :
ι → ι
.
λ x11 .
setsum
(
setsum
(
x10
x11
)
0
)
(
x7
(
x0
(
λ x12 .
x12
)
0
(
λ x12 :
ι → ι
.
x9
0
)
(
λ x12 :
ι → ι
.
λ x13 .
x1
(
λ x14 :
ι → ι
.
λ x15 x16 .
0
)
0
(
λ x14 x15 :
ι → ι
.
λ x16 .
0
)
0
)
(
setsum
0
0
)
(
x2
(
λ x12 x13 x14 x15 .
0
)
0
(
λ x12 :
ι →
ι → ι
.
0
)
)
)
(
setsum
(
Inj0
0
)
0
)
)
)
(
Inj0
(
x7
(
x0
(
λ x9 .
x1
(
λ x10 :
ι → ι
.
λ x11 x12 .
0
)
0
(
λ x10 x11 :
ι → ι
.
λ x12 .
0
)
0
)
x6
(
λ x9 :
ι → ι
.
setsum
0
0
)
(
λ x9 :
ι → ι
.
λ x10 .
setsum
0
0
)
(
x5
0
)
(
x3
(
λ x9 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
0
)
0
)
)
0
)
)
)
⟶
False
(proof)
Theorem
d5be2..
:
∀ x0 :
(
(
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι → ι
)
→ ι
)
→
ι → ι
.
∀ x1 :
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x2 :
(
(
(
ι →
ι → ι
)
→ ι
)
→
ι →
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι → ι
.
∀ x3 :
(
ι → ι
)
→
ι → ι
.
(
∀ x4 x5 .
∀ x6 :
(
(
ι →
ι → ι
)
→
ι → ι
)
→
(
ι →
ι → ι
)
→
ι →
ι → ι
.
∀ x7 :
ι →
(
ι → ι
)
→
ι → ι
.
x3
(
λ x9 .
setsum
(
x1
(
λ x10 .
0
)
(
λ x10 .
x7
(
x2
(
λ x11 :
(
ι →
ι → ι
)
→ ι
.
λ x12 .
λ x13 :
(
ι → ι
)
→ ι
.
0
)
0
)
(
λ x11 .
x10
)
(
Inj1
0
)
)
)
(
setsum
(
x1
(
λ x10 .
setsum
0
0
)
(
λ x10 .
x3
(
λ x11 .
0
)
0
)
)
(
setsum
0
(
x7
0
(
λ x10 .
0
)
0
)
)
)
)
(
x1
(
λ x9 .
Inj1
(
x1
(
λ x10 .
x6
(
λ x11 :
ι →
ι → ι
.
λ x12 .
0
)
(
λ x11 x12 .
0
)
0
0
)
(
λ x10 .
0
)
)
)
(
λ x9 .
x7
0
(
λ x10 .
x0
(
λ x11 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι → ι
.
x10
)
0
)
0
)
)
=
x1
(
λ x9 .
Inj0
(
setsum
x9
(
Inj0
(
Inj1
0
)
)
)
)
(
λ x9 .
x5
)
)
⟶
(
∀ x4 x5 :
ι → ι
.
∀ x6 x7 .
x3
(
λ x9 .
0
)
x7
=
setsum
0
0
)
⟶
(
∀ x4 x5 .
∀ x6 :
ι →
ι → ι
.
∀ x7 :
ι → ι
.
x2
(
λ x9 :
(
ι →
ι → ι
)
→ ι
.
λ x10 .
λ x11 :
(
ι → ι
)
→ ι
.
setsum
(
x1
(
λ x12 .
setsum
(
x0
(
λ x13 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι → ι
.
0
)
0
)
x10
)
(
λ x12 .
x1
(
λ x13 .
0
)
(
λ x13 .
x0
(
λ x14 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι → ι
.
0
)
0
)
)
)
(
Inj1
(
setsum
0
(
x2
(
λ x12 :
(
ι →
ι → ι
)
→ ι
.
λ x13 .
λ x14 :
(
ι → ι
)
→ ι
.
0
)
0
)
)
)
)
(
setsum
x5
(
Inj0
x4
)
)
=
x6
(
x0
(
λ x9 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι → ι
.
x6
(
x2
(
λ x10 :
(
ι →
ι → ι
)
→ ι
.
λ x11 .
λ x12 :
(
ι → ι
)
→ ι
.
x11
)
x5
)
0
)
(
x7
(
setsum
(
setsum
0
0
)
(
Inj1
0
)
)
)
)
(
Inj1
0
)
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
ι →
(
ι → ι
)
→ ι
.
x2
(
λ x9 :
(
ι →
ι → ι
)
→ ι
.
λ x10 .
λ x11 :
(
ι → ι
)
→ ι
.
0
)
(
x0
(
λ x9 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι → ι
.
x3
(
λ x10 .
x10
)
x5
)
(
setsum
x4
(
x2
(
λ x9 :
(
ι →
ι → ι
)
→ ι
.
λ x10 .
λ x11 :
(
ι → ι
)
→ ι
.
setsum
0
0
)
(
Inj1
0
)
)
)
)
=
x0
(
λ x9 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι → ι
.
Inj1
(
setsum
x6
0
)
)
(
setsum
(
setsum
(
x7
(
x0
(
λ x9 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι → ι
.
0
)
0
)
(
λ x9 .
x6
)
)
0
)
x5
)
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
∀ x7 .
x1
(
λ x9 .
x0
(
λ x10 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι → ι
.
x7
)
(
setsum
0
0
)
)
(
λ x9 .
setsum
(
x5
(
x0
(
λ x10 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι → ι
.
x2
(
λ x11 :
(
ι →
ι → ι
)
→ ι
.
λ x12 .
λ x13 :
(
ι → ι
)
→ ι
.
0
)
0
)
(
setsum
0
0
)
)
)
(
x3
(
λ x10 .
0
)
(
x3
(
λ x10 .
x0
(
λ x11 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι → ι
.
0
)
0
)
(
x3
(
λ x10 .
0
)
0
)
)
)
)
=
x0
(
λ x9 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι → ι
.
Inj1
(
Inj0
0
)
)
(
x1
(
λ x9 .
x6
(
Inj0
0
)
(
λ x10 :
ι → ι
.
λ x11 .
setsum
(
x0
(
λ x12 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι → ι
.
0
)
0
)
(
x10
0
)
)
0
0
)
(
λ x9 .
Inj0
0
)
)
)
⟶
(
∀ x4 x5 x6 x7 .
x1
(
λ x9 .
x3
(
λ x10 .
x3
(
λ x11 .
x0
(
λ x12 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι → ι
.
0
)
0
)
x6
)
x6
)
(
setsum
0
)
=
setsum
(
x0
(
λ x9 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι → ι
.
0
)
(
setsum
(
Inj0
(
setsum
0
0
)
)
0
)
)
0
)
⟶
(
∀ x4 :
(
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
∀ x5 :
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x6 .
∀ x7 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
x0
(
λ x9 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι → ι
.
Inj0
(
x5
(
setsum
(
setsum
0
0
)
(
x1
(
λ x10 .
0
)
(
λ x10 .
0
)
)
)
(
λ x10 x11 .
0
)
(
λ x10 .
Inj0
0
)
)
)
0
=
Inj0
(
Inj1
0
)
)
⟶
(
∀ x4 :
(
ι →
(
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x5 :
ι → ι
.
∀ x6 .
∀ x7 :
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
x0
(
λ x9 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι → ι
.
x9
(
λ x10 :
(
ι → ι
)
→ ι
.
x9
(
λ x11 :
(
ι → ι
)
→ ι
.
x7
(
x9
(
λ x12 :
(
ι → ι
)
→ ι
.
0
)
0
)
(
λ x12 x13 .
Inj0
0
)
(
λ x12 .
x1
(
λ x13 .
0
)
(
λ x13 .
0
)
)
)
0
)
0
)
(
setsum
0
(
x3
(
λ x9 .
0
)
(
x1
(
λ x9 .
x7
0
(
λ x10 x11 .
0
)
(
λ x10 .
0
)
)
(
λ x9 .
x1
(
λ x10 .
0
)
(
λ x10 .
0
)
)
)
)
)
=
x7
(
x3
(
λ x9 .
0
)
(
x1
(
λ x9 .
Inj1
0
)
(
λ x9 .
setsum
(
x7
0
(
λ x10 x11 .
0
)
(
λ x10 .
0
)
)
x6
)
)
)
(
λ x9 x10 .
Inj0
(
setsum
(
setsum
(
x1
(
λ x11 .
0
)
(
λ x11 .
0
)
)
0
)
(
x7
x9
(
λ x11 x12 .
x1
(
λ x13 .
0
)
(
λ x13 .
0
)
)
(
λ x11 .
x10
)
)
)
)
(
λ x9 .
x2
(
λ x10 :
(
ι →
ι → ι
)
→ ι
.
λ x11 .
λ x12 :
(
ι → ι
)
→ ι
.
Inj1
(
x2
(
λ x13 :
(
ι →
ι → ι
)
→ ι
.
λ x14 .
λ x15 :
(
ι → ι
)
→ ι
.
x15
(
λ x16 .
0
)
)
(
x12
(
λ x13 .
0
)
)
)
)
(
x1
(
λ x10 .
x7
(
Inj1
0
)
(
λ x11 x12 .
0
)
(
λ x11 .
0
)
)
(
λ x10 .
x9
)
)
)
)
⟶
False
(proof)
Theorem
7087a..
:
∀ x0 :
(
(
(
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
)
→ ι
)
→
(
(
(
ι →
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
∀ 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
.
∀ x2 :
(
ι → ι
)
→
(
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
.
∀ x3 :
(
ι →
(
ι → ι
)
→
ι →
ι → ι
)
→
(
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→ ι
.
(
∀ x4 :
(
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→
ι → ι
.
∀ x5 :
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x6 x7 .
x3
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 x12 .
x3
(
λ x13 .
λ x14 :
ι → ι
.
λ x15 x16 .
0
)
(
λ x13 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x14 .
0
)
)
(
λ x9 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x10 .
x10
)
=
Inj1
(
Inj0
(
x4
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 .
x10
)
(
x1
(
λ x9 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→ ι
.
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 :
ι → ι
.
λ x12 x13 .
x2
(
λ x14 .
0
)
(
λ x14 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x15 :
(
ι → ι
)
→ ι
.
0
)
)
(
λ x9 .
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 .
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
(
(
ι →
ι → ι
)
→ ι
)
→ ι
.
∀ x6 .
∀ x7 :
ι →
ι → ι
.
x3
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 x12 .
setsum
(
setsum
x11
0
)
0
)
(
λ x9 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x10 .
0
)
=
x5
(
λ x9 :
ι →
ι → ι
.
0
)
)
⟶
(
∀ x4 x5 x6 x7 .
x2
(
λ x9 .
x0
(
λ x10 :
(
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
Inj1
(
setsum
(
Inj0
0
)
(
Inj1
0
)
)
)
(
λ x10 :
(
ι →
ι → ι
)
→
ι → ι
.
Inj1
0
)
)
(
λ x9 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x10 :
(
ι → ι
)
→ ι
.
x1
(
λ x11 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→ ι
.
λ x12 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x13 :
ι → ι
.
λ x14 x15 .
Inj1
(
setsum
(
x13
0
)
0
)
)
(
λ x11 .
λ x12 :
(
ι → ι
)
→
ι → ι
.
λ x13 .
x10
(
λ x14 .
0
)
)
)
=
x1
(
λ x9 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→ ι
.
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 :
ι → ι
.
λ x12 x13 .
Inj0
0
)
(
λ x9 .
λ x10 :
(
ι → ι
)
→
ι → ι
.
Inj1
)
)
⟶
(
∀ x4 :
(
ι →
ι → ι
)
→ ι
.
∀ x5 :
ι →
ι →
ι →
ι → ι
.
∀ x6 .
∀ x7 :
ι →
ι → ι
.
x2
(
λ x9 .
x1
(
λ x10 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→ ι
.
λ x11 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x12 :
ι → ι
.
λ x13 x14 .
x12
(
x3
(
λ x15 .
λ x16 :
ι → ι
.
λ x17 x18 .
0
)
(
λ x15 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x16 .
setsum
0
0
)
)
)
(
λ x10 .
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 .
x12
)
)
(
λ x9 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x10 :
(
ι → ι
)
→ ι
.
x0
(
λ x11 :
(
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
x2
(
λ x12 .
x12
)
(
λ x12 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x13 :
(
ι → ι
)
→ ι
.
0
)
)
(
λ x11 :
(
ι →
ι → ι
)
→
ι → ι
.
x11
(
λ x12 x13 .
0
)
(
x9
(
λ x12 x13 .
0
)
(
λ x12 .
0
)
(
x11
(
λ x12 x13 .
0
)
0
)
)
)
)
=
x0
(
λ x9 :
(
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
setsum
0
(
x7
0
(
x2
(
λ x10 .
x9
(
λ x11 .
0
)
(
λ x11 :
ι → ι
.
0
)
(
λ x11 .
0
)
)
(
λ x10 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x11 :
(
ι → ι
)
→ ι
.
0
)
)
)
)
(
λ x9 :
(
ι →
ι → ι
)
→
ι → ι
.
x7
(
x7
(
Inj0
(
Inj0
0
)
)
(
x2
(
λ x10 .
x7
0
0
)
(
λ x10 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x11 :
(
ι → ι
)
→ ι
.
setsum
0
0
)
)
)
(
Inj0
(
Inj1
(
x1
(
λ x10 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→ ι
.
λ x11 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x12 :
ι → ι
.
λ x13 x14 .
0
)
(
λ x10 .
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 .
0
)
)
)
)
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
ι → ι
.
∀ x7 :
ι →
(
ι → ι
)
→ ι
.
x1
(
λ x9 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→ ι
.
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 :
ι → ι
.
λ x12 x13 .
0
)
(
λ x9 .
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 .
0
)
=
Inj0
(
x6
0
)
)
⟶
(
∀ x4 x5 x6 x7 .
x1
(
λ x9 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→ ι
.
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 :
ι → ι
.
λ x12 x13 .
0
)
(
λ x9 .
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 .
x3
(
λ x12 .
λ x13 :
ι → ι
.
λ x14 x15 .
x15
)
(
λ x12 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x13 .
Inj1
(
x0
(
λ x14 :
(
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
setsum
0
0
)
(
λ x14 :
(
ι →
ι → ι
)
→
ι → ι
.
0
)
)
)
)
=
setsum
(
x1
(
λ x9 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→ ι
.
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 :
ι → ι
.
λ x12 x13 .
x11
(
Inj0
(
x10
(
λ x14 :
ι → ι
.
0
)
)
)
)
(
λ x9 .
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 .
0
)
)
(
x1
(
λ x9 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→ ι
.
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 :
ι → ι
.
λ x12 x13 .
x1
(
λ x14 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→ ι
.
λ x15 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x16 :
ι → ι
.
λ x17 x18 .
setsum
(
x2
(
λ x19 .
0
)
(
λ x19 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x20 :
(
ι → ι
)
→ ι
.
0
)
)
(
x1
(
λ x19 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→ ι
.
λ x20 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x21 :
ι → ι
.
λ x22 x23 .
0
)
(
λ x19 .
λ x20 :
(
ι → ι
)
→
ι → ι
.
λ x21 .
0
)
)
)
(
λ x14 .
λ x15 :
(
ι → ι
)
→
ι → ι
.
λ x16 .
x13
)
)
(
λ x9 .
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 .
x0
(
λ x12 :
(
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
Inj0
x9
)
(
λ x12 :
(
ι →
ι → ι
)
→
ι → ι
.
0
)
)
)
)
⟶
(
∀ x4 x5 x6 x7 .
x0
(
λ x9 :
(
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
x1
(
λ x10 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→ ι
.
λ x11 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x12 :
ι → ι
.
λ x13 x14 .
x12
(
x2
(
λ x15 .
0
)
(
λ x15 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x16 :
(
ι → ι
)
→ ι
.
0
)
)
)
(
λ x10 .
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 .
0
)
)
(
λ x9 :
(
ι →
ι → ι
)
→
ι → ι
.
setsum
(
Inj0
(
Inj1
x7
)
)
(
setsum
(
setsum
(
x9
(
λ x10 x11 .
0
)
0
)
(
setsum
0
0
)
)
0
)
)
=
x1
(
λ x9 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→ ι
.
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 :
ι → ι
.
λ x12 x13 .
setsum
(
x10
(
λ x14 :
ι → ι
.
x14
(
Inj1
0
)
)
)
(
x1
(
λ x14 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→ ι
.
λ x15 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x16 :
ι → ι
.
λ x17 x18 .
x1
(
λ x19 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→ ι
.
λ x20 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x21 :
ι → ι
.
λ x22 x23 .
x23
)
(
λ x19 .
λ x20 :
(
ι → ι
)
→
ι → ι
.
λ x21 .
Inj0
0
)
)
(
λ x14 .
λ x15 :
(
ι → ι
)
→
ι → ι
.
λ x16 .
Inj0
(
Inj1
0
)
)
)
)
(
λ x9 .
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 .
Inj1
0
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 x6 x7 .
x0
(
λ x9 :
(
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
x3
(
λ x10 .
λ x11 :
ι → ι
.
λ x12 x13 .
x1
(
λ x14 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→ ι
.
λ x15 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x16 :
ι → ι
.
λ x17 x18 .
0
)
(
λ x14 .
λ x15 :
(
ι → ι
)
→
ι → ι
.
λ x16 .
x1
(
λ x17 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→ ι
.
λ x18 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x19 :
ι → ι
.
λ x20 x21 .
x21
)
(
λ x17 .
λ x18 :
(
ι → ι
)
→
ι → ι
.
λ x19 .
x16
)
)
)
(
λ x10 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x11 .
x11
)
)
(
λ x9 :
(
ι →
ι → ι
)
→
ι → ι
.
x0
(
λ x10 :
(
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
x7
)
(
λ x10 :
(
ι →
ι → ι
)
→
ι → ι
.
0
)
)
=
Inj1
(
x4
(
setsum
0
0
)
)
)
⟶
False
(proof)
Theorem
479b0..
:
∀ x0 :
(
ι → ι
)
→
(
ι → ι
)
→
(
(
ι →
ι → ι
)
→ ι
)
→ ι
.
∀ x1 :
(
ι →
(
ι →
(
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
ι → ι
.
∀ x2 :
(
ι → ι
)
→
ι → ι
.
∀ x3 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
(
∀ x4 x5 x6 x7 .
x3
(
λ x9 :
(
ι → ι
)
→ ι
.
Inj0
x6
)
(
λ x9 .
x9
)
(
x0
(
λ x9 .
x6
)
(
λ x9 .
x0
(
λ x10 .
0
)
(
λ x10 .
Inj1
(
setsum
0
0
)
)
(
λ x10 :
ι →
ι → ι
.
x1
(
λ x11 .
λ x12 :
ι →
(
ι → ι
)
→ ι
.
λ x13 :
ι →
ι → ι
.
λ x14 :
ι → ι
.
x3
(
λ x15 :
(
ι → ι
)
→ ι
.
0
)
(
λ x15 .
0
)
0
)
0
)
)
(
λ x9 :
ι →
ι → ι
.
x0
(
λ x10 .
0
)
(
λ x10 .
setsum
(
Inj1
0
)
x6
)
(
λ x10 :
ι →
ι → ι
.
Inj0
0
)
)
)
=
x0
(
λ x9 .
x9
)
(
λ x9 .
x9
)
(
λ x9 :
ι →
ι → ι
.
setsum
(
x3
(
λ x10 :
(
ι → ι
)
→ ι
.
x7
)
(
λ x10 .
0
)
x6
)
(
x9
(
x1
(
λ x10 .
λ x11 :
ι →
(
ι → ι
)
→ ι
.
λ x12 :
ι →
ι → ι
.
λ x13 :
ι → ι
.
0
)
x5
)
0
)
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x5 x6 .
∀ x7 :
ι →
(
ι →
ι → ι
)
→ ι
.
x3
(
λ x9 :
(
ι → ι
)
→ ι
.
x9
(
λ x10 .
x10
)
)
(
λ x9 .
x3
(
λ x10 :
(
ι → ι
)
→ ι
.
x7
(
setsum
0
(
x7
0
(
λ x11 x12 .
0
)
)
)
(
λ x11 x12 .
0
)
)
(
λ x10 .
x9
)
(
Inj1
x6
)
)
0
=
setsum
x6
x5
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι →
ι →
ι → ι
.
∀ x5 .
∀ x6 :
ι → ι
.
∀ x7 :
(
(
ι →
ι → ι
)
→ ι
)
→
ι → ι
.
x2
(
λ x9 .
x1
(
λ x10 .
λ x11 :
ι →
(
ι → ι
)
→ ι
.
λ x12 :
ι →
ι → ι
.
λ x13 :
ι → ι
.
Inj1
(
x13
0
)
)
(
x7
(
λ x10 :
ι →
ι → ι
.
setsum
(
x0
(
λ x11 .
0
)
(
λ x11 .
0
)
(
λ x11 :
ι →
ι → ι
.
0
)
)
(
x7
(
λ x11 :
ι →
ι → ι
.
0
)
0
)
)
(
Inj1
(
Inj1
0
)
)
)
)
(
x1
(
λ x9 .
λ x10 :
ι →
(
ι → ι
)
→ ι
.
λ x11 :
ι →
ι → ι
.
λ x12 :
ι → ι
.
setsum
(
x2
(
λ x13 .
0
)
(
x3
(
λ x13 :
(
ι → ι
)
→ ι
.
0
)
(
λ x13 .
0
)
0
)
)
0
)
0
)
=
Inj0
0
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 x7 .
x2
(
λ x9 .
x7
)
(
x0
(
λ x9 .
x0
(
λ x10 .
setsum
x7
0
)
(
λ x10 .
x0
(
λ x11 .
x1
(
λ x12 .
λ x13 :
ι →
(
ι → ι
)
→ ι
.
λ x14 :
ι →
ι → ι
.
λ x15 :
ι → ι
.
0
)
0
)
(
λ x11 .
setsum
0
0
)
(
λ x11 :
ι →
ι → ι
.
0
)
)
(
λ x10 :
ι →
ι → ι
.
Inj1
(
Inj1
0
)
)
)
(
λ x9 .
x6
)
(
λ x9 :
ι →
ι → ι
.
x5
0
)
)
=
Inj1
(
x2
(
λ x9 .
setsum
x7
(
Inj1
(
x5
0
)
)
)
0
)
)
⟶
(
∀ x4 .
∀ x5 :
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x6 x7 .
x1
(
λ x9 .
λ x10 :
ι →
(
ι → ι
)
→ ι
.
λ x11 :
ι →
ι → ι
.
λ x12 :
ι → ι
.
x2
(
λ x13 .
x12
(
x3
(
λ x14 :
(
ι → ι
)
→ ι
.
x3
(
λ x15 :
(
ι → ι
)
→ ι
.
0
)
(
λ x15 .
0
)
0
)
(
λ x14 .
0
)
(
Inj0
0
)
)
)
0
)
(
Inj0
x7
)
=
Inj1
(
Inj1
(
setsum
x7
(
x2
(
λ x9 .
Inj0
0
)
(
x1
(
λ x9 .
λ x10 :
ι →
(
ι → ι
)
→ ι
.
λ x11 :
ι →
ι → ι
.
λ x12 :
ι → ι
.
0
)
0
)
)
)
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→ ι
.
∀ x5 .
∀ x6 x7 :
ι → ι
.
x1
(
λ x9 .
λ x10 :
ι →
(
ι → ι
)
→ ι
.
λ x11 :
ι →
ι → ι
.
λ x12 :
ι → ι
.
x10
0
(
λ x13 .
0
)
)
0
=
x5
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
∀ x5 :
ι → ι
.
∀ x6 :
(
ι → ι
)
→
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x7 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
x0
(
λ x9 .
0
)
(
λ x9 .
x0
(
λ x10 .
x6
(
λ x11 .
0
)
(
λ x11 .
0
)
(
λ x11 .
setsum
(
x3
(
λ x12 :
(
ι → ι
)
→ ι
.
0
)
(
λ x12 .
0
)
0
)
(
setsum
0
0
)
)
(
x2
(
λ x11 .
x9
)
(
x3
(
λ x11 :
(
ι → ι
)
→ ι
.
0
)
(
λ x11 .
0
)
0
)
)
)
(
x6
(
λ x10 .
x10
)
(
λ x10 .
Inj0
0
)
(
λ x10 .
x1
(
λ x11 .
λ x12 :
ι →
(
ι → ι
)
→ ι
.
λ x13 :
ι →
ι → ι
.
λ x14 :
ι → ι
.
0
)
(
x1
(
λ x11 .
λ x12 :
ι →
(
ι → ι
)
→ ι
.
λ x13 :
ι →
ι → ι
.
λ x14 :
ι → ι
.
0
)
0
)
)
)
(
λ x10 :
ι →
ι → ι
.
0
)
)
(
λ x9 :
ι →
ι → ι
.
0
)
=
Inj1
(
x3
(
λ x9 :
(
ι → ι
)
→ ι
.
x5
(
setsum
0
(
x6
(
λ x10 .
0
)
(
λ x10 .
0
)
(
λ x10 .
0
)
0
)
)
)
(
λ x9 .
x7
(
λ x10 .
λ x11 :
ι → ι
.
Inj1
x9
)
(
x1
(
λ x10 .
λ x11 :
ι →
(
ι → ι
)
→ ι
.
λ x12 :
ι →
ι → ι
.
λ x13 :
ι → ι
.
Inj1
0
)
(
Inj1
0
)
)
0
)
(
setsum
(
Inj0
(
x7
(
λ x9 .
λ x10 :
ι → ι
.
0
)
0
0
)
)
(
Inj1
0
)
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 :
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x6 :
ι →
(
ι → ι
)
→
ι →
ι → ι
.
∀ x7 .
x0
(
λ x9 .
x3
(
λ x10 :
(
ι → ι
)
→ ι
.
setsum
(
x10
(
λ x11 .
0
)
)
(
x3
(
λ x11 :
(
ι → ι
)
→ ι
.
x10
(
λ x12 .
0
)
)
(
λ x11 .
x3
(
λ x12 :
(
ι → ι
)
→ ι
.
0
)
(
λ x12 .
0
)
0
)
0
)
)
(
λ x10 .
0
)
(
setsum
(
x3
(
λ x10 :
(
ι → ι
)
→ ι
.
0
)
(
λ x10 .
0
)
(
Inj1
0
)
)
(
Inj1
0
)
)
)
(
λ x9 .
x2
(
λ x10 .
x2
(
setsum
(
setsum
0
0
)
)
0
)
(
setsum
x7
0
)
)
(
λ x9 :
ι →
ι → ι
.
x5
(
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 :
ι → ι
.
λ x12 .
x1
(
λ x13 .
λ x14 :
ι →
(
ι → ι
)
→ ι
.
λ x15 :
ι →
ι → ι
.
λ x16 :
ι → ι
.
Inj1
0
)
(
Inj1
0
)
)
)
=
setsum
0
(
x2
(
λ x9 .
0
)
0
)
)
⟶
False
(proof)
Theorem
ea880..
:
∀ x0 :
(
ι →
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι →
ι → ι
)
→
ι →
ι →
ι →
ι →
ι → ι
.
∀ x1 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
∀ x2 :
(
ι →
ι → ι
)
→
ι → ι
.
∀ x3 :
(
(
ι → ι
)
→
ι →
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
(
ι →
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
(
∀ x4 :
ι → ι
.
∀ x5 :
(
ι → ι
)
→ ι
.
∀ x6 .
∀ x7 :
(
(
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
x3
(
λ x9 :
ι → ι
.
λ x10 .
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 :
ι → ι
.
0
)
(
λ x9 .
λ x10 :
(
ι → ι
)
→ ι
.
x0
(
λ x11 .
λ x12 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x13 x14 .
x2
(
λ x15 x16 .
x15
)
0
)
(
setsum
(
x10
(
λ x11 .
0
)
)
(
x2
(
λ x11 x12 .
0
)
(
setsum
0
0
)
)
)
(
setsum
(
Inj1
x6
)
x9
)
(
setsum
(
setsum
(
x0
(
λ x11 .
λ x12 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x13 x14 .
0
)
0
0
0
0
0
)
(
Inj0
0
)
)
0
)
(
x10
(
λ x11 .
x2
(
λ x12 x13 .
Inj0
0
)
0
)
)
0
)
(
λ x9 .
x6
)
=
x0
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 x12 .
setsum
(
x2
(
λ x13 x14 .
setsum
(
setsum
0
0
)
(
x0
(
λ x15 .
λ x16 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x17 x18 .
0
)
0
0
0
0
0
)
)
(
Inj1
x11
)
)
(
Inj0
(
Inj1
(
x2
(
λ x13 x14 .
0
)
0
)
)
)
)
(
setsum
(
Inj1
0
)
(
x1
(
λ x9 :
ι → ι
.
setsum
x6
(
setsum
0
0
)
)
0
)
)
(
setsum
(
x0
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 x12 .
0
)
0
(
Inj1
(
x1
(
λ x9 :
ι → ι
.
0
)
0
)
)
(
setsum
(
x4
0
)
0
)
(
x7
(
λ x9 x10 :
ι → ι
.
Inj1
0
)
(
λ x9 x10 .
Inj0
0
)
)
(
x0
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 x12 .
Inj0
0
)
(
x4
0
)
(
x2
(
λ x9 x10 .
0
)
0
)
(
Inj1
0
)
(
x7
(
λ x9 x10 :
ι → ι
.
0
)
(
λ x9 x10 .
0
)
)
x6
)
)
(
x5
(
λ x9 .
Inj1
0
)
)
)
(
x5
(
λ x9 .
x0
(
λ x10 .
λ x11 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x12 x13 .
x2
(
λ x14 x15 .
Inj1
0
)
(
x2
(
λ x14 x15 .
0
)
0
)
)
(
setsum
(
x0
(
λ x10 .
λ x11 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x12 x13 .
0
)
0
0
0
0
0
)
x6
)
(
setsum
(
x3
(
λ x10 :
ι → ι
.
λ x11 .
λ x12 :
(
ι → ι
)
→
ι → ι
.
λ x13 :
ι → ι
.
0
)
(
λ x10 .
λ x11 :
(
ι → ι
)
→ ι
.
0
)
(
λ x10 .
0
)
)
(
x0
(
λ x10 .
λ x11 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x12 x13 .
0
)
0
0
0
0
0
)
)
x6
0
0
)
)
(
setsum
(
x7
(
λ x9 x10 :
ι → ι
.
Inj1
(
setsum
0
0
)
)
(
λ x9 x10 .
setsum
(
x2
(
λ x11 x12 .
0
)
0
)
0
)
)
(
x0
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 x12 .
0
)
(
x1
(
λ x9 :
ι → ι
.
x0
(
λ x10 .
λ x11 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x12 x13 .
0
)
0
0
0
0
0
)
0
)
(
x2
(
λ x9 x10 .
Inj1
0
)
(
setsum
0
0
)
)
0
0
0
)
)
(
x2
(
λ x9 x10 .
x9
)
(
x4
(
setsum
0
(
x2
(
λ x9 x10 .
0
)
0
)
)
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 .
∀ x6 :
ι → ι
.
∀ x7 :
(
ι → ι
)
→ ι
.
x3
(
λ x9 :
ι → ι
.
λ x10 .
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 :
ι → ι
.
x2
(
λ x13 x14 .
0
)
(
x11
(
λ x13 .
x10
)
0
)
)
(
λ x9 .
λ x10 :
(
ι → ι
)
→ ι
.
0
)
(
λ x9 .
Inj0
(
x0
(
λ x10 .
λ x11 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x12 x13 .
0
)
(
setsum
(
setsum
0
0
)
x5
)
0
(
Inj0
(
Inj1
0
)
)
(
x2
(
λ x10 x11 .
0
)
(
x6
0
)
)
(
x2
(
λ x10 x11 .
x0
(
λ x12 .
λ x13 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x14 x15 .
0
)
0
0
0
0
0
)
x5
)
)
)
=
Inj0
(
x6
(
x7
(
λ x9 .
x7
(
λ x10 .
x10
)
)
)
)
)
⟶
(
∀ x4 x5 .
∀ x6 x7 :
ι → ι
.
x2
(
λ x9 .
Inj0
)
0
=
x5
)
⟶
(
∀ x4 .
∀ x5 :
(
(
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
ι → ι
.
∀ x6 :
(
ι →
ι →
ι → ι
)
→
ι →
ι → ι
.
∀ x7 .
x2
(
λ x9 x10 .
x10
)
x7
=
x7
)
⟶
(
∀ x4 .
∀ x5 :
ι →
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
∀ x6 .
∀ x7 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
x1
(
λ x9 :
ι → ι
.
x0
(
λ x10 .
λ x11 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x12 x13 .
0
)
(
setsum
(
Inj0
(
x1
(
λ x10 :
ι → ι
.
0
)
0
)
)
(
x1
(
λ x10 :
ι → ι
.
0
)
(
x1
(
λ x10 :
ι → ι
.
0
)
0
)
)
)
0
(
setsum
(
x0
(
λ x10 .
λ x11 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x12 x13 .
x0
(
λ x14 .
λ x15 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x16 x17 .
0
)
0
0
0
0
0
)
(
x5
0
(
λ x10 :
ι → ι
.
0
)
0
0
)
(
x3
(
λ x10 :
ι → ι
.
λ x11 .
λ x12 :
(
ι → ι
)
→
ι → ι
.
λ x13 :
ι → ι
.
0
)
(
λ x10 .
λ x11 :
(
ι → ι
)
→ ι
.
0
)
(
λ x10 .
0
)
)
0
0
(
setsum
0
0
)
)
(
x9
0
)
)
(
x2
(
λ x10 x11 .
0
)
(
Inj0
x6
)
)
0
)
0
=
x0
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 x12 .
x9
)
(
x3
(
λ x9 :
ι → ι
.
λ x10 .
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 :
ι → ι
.
setsum
(
x1
(
λ x13 :
ι → ι
.
setsum
0
0
)
(
x9
0
)
)
(
x0
(
λ x13 .
λ x14 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x15 x16 .
x3
(
λ x17 :
ι → ι
.
λ x18 .
λ x19 :
(
ι → ι
)
→
ι → ι
.
λ x20 :
ι → ι
.
0
)
(
λ x17 .
λ x18 :
(
ι → ι
)
→ ι
.
0
)
(
λ x17 .
0
)
)
(
x9
0
)
(
x1
(
λ x13 :
ι → ι
.
0
)
0
)
(
x11
(
λ x13 .
0
)
0
)
0
(
x0
(
λ x13 .
λ x14 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x15 x16 .
0
)
0
0
0
0
0
)
)
)
(
λ x9 .
λ x10 :
(
ι → ι
)
→ ι
.
setsum
(
Inj1
x6
)
(
Inj1
0
)
)
(
λ x9 .
setsum
(
x5
0
(
λ x10 :
ι → ι
.
Inj0
0
)
0
(
setsum
0
0
)
)
(
Inj1
(
x7
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 :
ι → ι
.
0
)
)
)
)
)
(
Inj1
(
setsum
(
setsum
(
x0
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 x12 .
0
)
0
0
0
0
0
)
(
x5
0
(
λ x9 :
ι → ι
.
0
)
0
0
)
)
(
Inj1
(
x2
(
λ x9 x10 .
0
)
0
)
)
)
)
(
x2
(
λ x9 x10 .
x10
)
(
x5
(
setsum
(
x3
(
λ x9 :
ι → ι
.
λ x10 .
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 :
ι → ι
.
0
)
(
λ x9 .
λ x10 :
(
ι → ι
)
→ ι
.
0
)
(
λ x9 .
0
)
)
(
x7
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 :
ι → ι
.
0
)
)
)
(
λ x9 :
ι → ι
.
x0
(
λ x10 .
λ x11 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x12 x13 .
0
)
0
x6
x6
(
x3
(
λ x10 :
ι → ι
.
λ x11 .
λ x12 :
(
ι → ι
)
→
ι → ι
.
λ x13 :
ι → ι
.
0
)
(
λ x10 .
λ x11 :
(
ι → ι
)
→ ι
.
0
)
(
λ x10 .
0
)
)
(
x5
0
(
λ x10 :
ι → ι
.
0
)
0
0
)
)
0
(
x3
(
λ x9 :
ι → ι
.
λ x10 .
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 :
ι → ι
.
setsum
0
0
)
(
λ x9 .
λ x10 :
(
ι → ι
)
→ ι
.
Inj0
0
)
(
λ x9 .
x1
(
λ x10 :
ι → ι
.
0
)
0
)
)
)
)
(
setsum
(
x0
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 x12 .
0
)
(
Inj0
(
x3
(
λ x9 :
ι → ι
.
λ x10 .
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 :
ι → ι
.
0
)
(
λ x9 .
λ x10 :
(
ι → ι
)
→ ι
.
0
)
(
λ x9 .
0
)
)
)
(
Inj0
(
x2
(
λ x9 x10 .
0
)
0
)
)
(
Inj0
(
x7
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 :
ι → ι
.
0
)
)
)
(
x3
(
λ x9 :
ι → ι
.
λ x10 .
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 :
ι → ι
.
x2
(
λ x13 x14 .
0
)
0
)
(
λ x9 .
λ x10 :
(
ι → ι
)
→ ι
.
x2
(
λ x11 x12 .
0
)
0
)
(
λ x9 .
x0
(
λ x10 .
λ x11 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x12 x13 .
0
)
0
0
0
0
0
)
)
(
x7
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 :
ι → ι
.
x10
0
)
)
)
(
x5
0
(
λ x9 :
ι → ι
.
0
)
(
x0
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 x12 .
0
)
0
(
setsum
0
0
)
(
x7
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 :
ι → ι
.
0
)
)
(
x7
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 :
ι → ι
.
0
)
)
(
setsum
0
0
)
)
0
)
)
(
setsum
(
x2
(
λ x9 x10 .
0
)
(
x0
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 x12 .
0
)
0
0
(
Inj0
0
)
(
x3
(
λ x9 :
ι → ι
.
λ x10 .
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 :
ι → ι
.
0
)
(
λ x9 .
λ x10 :
(
ι → ι
)
→ ι
.
0
)
(
λ x9 .
0
)
)
x4
)
)
(
setsum
0
0
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 x6 .
∀ x7 :
ι →
ι → ι
.
x1
(
λ x9 :
ι → ι
.
x1
(
λ x10 :
ι → ι
.
setsum
(
Inj0
(
x7
0
0
)
)
(
setsum
(
x3
(
λ x11 :
ι → ι
.
λ x12 .
λ x13 :
(
ι → ι
)
→
ι → ι
.
λ x14 :
ι → ι
.
0
)
(
λ x11 .
λ x12 :
(
ι → ι
)
→ ι
.
0
)
(
λ x11 .
0
)
)
0
)
)
(
x7
(
x0
(
λ x10 .
λ x11 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x12 x13 .
0
)
(
x3
(
λ x10 :
ι → ι
.
λ x11 .
λ x12 :
(
ι → ι
)
→
ι → ι
.
λ x13 :
ι → ι
.
0
)
(
λ x10 .
λ x11 :
(
ι → ι
)
→ ι
.
0
)
(
λ x10 .
0
)
)
(
x7
0
0
)
0
(
Inj1
0
)
0
)
(
x2
(
λ x10 x11 .
x1
(
λ x12 :
ι → ι
.
0
)
0
)
(
x7
0
0
)
)
)
)
x5
=
setsum
x6
(
Inj1
(
x4
x5
)
)
)
⟶
(
∀ x4 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
∀ x5 .
∀ x6 :
(
ι → ι
)
→
ι → ι
.
∀ x7 :
ι → ι
.
x0
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 x12 .
x11
)
(
x1
(
λ x9 :
ι → ι
.
0
)
(
setsum
x5
(
x3
(
λ x9 :
ι → ι
.
λ x10 .
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 :
ι → ι
.
x9
0
)
(
λ x9 .
λ x10 :
(
ι → ι
)
→ ι
.
x10
(
λ x11 .
0
)
)
(
λ x9 .
Inj0
0
)
)
)
)
(
x6
(
λ x9 .
0
)
0
)
(
x4
(
setsum
0
(
setsum
(
x6
(
λ x9 .
0
)
0
)
(
x0
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 x12 .
0
)
0
0
0
0
0
)
)
)
(
λ x9 :
ι → ι
.
λ x10 .
x7
(
setsum
0
(
x6
(
λ x11 .
0
)
0
)
)
)
(
Inj0
(
x2
(
λ x9 x10 .
setsum
0
0
)
(
x2
(
λ x9 x10 .
0
)
0
)
)
)
)
(
x6
(
λ x9 .
0
)
(
x6
(
λ x9 .
0
)
(
Inj1
(
setsum
0
0
)
)
)
)
(
x1
(
λ x9 :
ι → ι
.
Inj1
(
setsum
0
(
x6
(
λ x10 .
0
)
0
)
)
)
(
x2
(
λ x9 x10 .
0
)
0
)
)
=
x6
(
λ x9 .
x5
)
(
Inj1
(
x6
(
λ x9 .
x9
)
(
Inj1
0
)
)
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x5 x6 .
∀ x7 :
(
ι →
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
x0
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 x12 .
x1
(
λ x13 :
ι → ι
.
Inj1
(
x10
(
λ x14 :
ι → ι
.
x2
(
λ x15 x16 .
0
)
0
)
)
)
(
x3
(
λ x13 :
ι → ι
.
λ x14 .
λ x15 :
(
ι → ι
)
→
ι → ι
.
λ x16 :
ι → ι
.
x15
(
λ x17 .
x14
)
(
Inj1
0
)
)
(
λ x13 .
λ x14 :
(
ι → ι
)
→ ι
.
0
)
(
λ x13 .
setsum
x13
(
x3
(
λ x14 :
ι → ι
.
λ x15 .
λ x16 :
(
ι → ι
)
→
ι → ι
.
λ x17 :
ι → ι
.
0
)
(
λ x14 .
λ x15 :
(
ι → ι
)
→ ι
.
0
)
(
λ x14 .
0
)
)
)
)
)
0
x5
(
x7
(
λ x9 x10 .
x1
(
λ x11 :
ι → ι
.
Inj0
0
)
x6
)
(
λ x9 :
ι → ι
.
λ x10 .
x3
(
λ x11 :
ι → ι
.
λ x12 .
λ x13 :
(
ι → ι
)
→
ι → ι
.
λ x14 :
ι → ι
.
x12
)
(
λ x11 .
λ x12 :
(
ι → ι
)
→ ι
.
x0
(
λ x13 .
λ x14 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x15 x16 .
x14
(
λ x17 :
ι → ι
.
0
)
)
x10
(
Inj1
0
)
(
setsum
0
0
)
(
setsum
0
0
)
0
)
(
λ x11 .
Inj1
(
x9
0
)
)
)
(
x0
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 x12 .
x1
(
λ x13 :
ι → ι
.
0
)
(
Inj1
0
)
)
(
Inj1
0
)
0
x6
0
(
Inj1
0
)
)
(
setsum
x5
0
)
)
(
x7
(
λ x9 x10 .
0
)
(
λ x9 :
ι → ι
.
λ x10 .
x9
0
)
0
(
x7
(
λ x9 x10 .
x7
(
λ x11 x12 .
0
)
(
λ x11 :
ι → ι
.
λ x12 .
setsum
0
0
)
(
Inj1
0
)
0
)
(
λ x9 :
ι → ι
.
λ x10 .
x9
(
Inj0
0
)
)
0
(
Inj1
(
x0
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 x12 .
0
)
0
0
0
0
0
)
)
)
)
x5
=
Inj0
(
x1
(
λ x9 :
ι → ι
.
0
)
0
)
)
⟶
False
(proof)
Theorem
5d624..
:
∀ x0 :
(
ι → ι
)
→
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
.
∀ x1 :
(
ι →
ι → ι
)
→
ι → ι
.
∀ x2 :
(
ι → ι
)
→
ι →
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x3 :
(
(
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
)
→ ι
)
→
ι →
ι →
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
(
∀ x4 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι →
ι → ι
.
∀ x5 x6 x7 .
x3
(
λ x9 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
x6
)
(
x3
(
λ x9 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
setsum
0
0
)
x7
(
x1
(
λ x9 x10 .
x10
)
(
x3
(
λ x9 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
x0
(
λ x10 .
0
)
(
λ x10 :
(
ι → ι
)
→ ι
.
0
)
)
x7
0
(
λ x9 :
ι → ι
.
λ x10 .
x6
)
0
x7
)
)
(
λ x9 :
ι → ι
.
λ x10 .
0
)
(
x3
(
λ x9 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
x5
)
(
x4
(
λ x9 :
(
ι → ι
)
→ ι
.
setsum
0
0
)
(
x2
(
λ x9 .
0
)
0
(
λ x9 .
0
)
(
λ x9 .
0
)
)
x7
)
(
x2
(
λ x9 .
x6
)
0
(
λ x9 .
Inj0
0
)
(
λ x9 .
setsum
0
0
)
)
(
λ x9 :
ι → ι
.
λ x10 .
x6
)
(
Inj0
0
)
(
x4
(
λ x9 :
(
ι → ι
)
→ ι
.
setsum
0
0
)
(
Inj0
0
)
(
x0
(
λ x9 .
0
)
(
λ x9 :
(
ι → ι
)
→ ι
.
0
)
)
)
)
(
x4
(
λ x9 :
(
ι → ι
)
→ ι
.
0
)
(
x0
(
λ x9 .
x3
(
λ x10 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
0
)
0
0
(
λ x10 :
ι → ι
.
λ x11 .
0
)
0
0
)
(
λ x9 :
(
ι → ι
)
→ ι
.
Inj0
0
)
)
x6
)
)
(
x2
(
λ x9 .
0
)
(
setsum
(
setsum
x5
(
setsum
0
0
)
)
(
x2
(
λ x9 .
x5
)
(
Inj0
0
)
(
λ x9 .
x7
)
(
λ x9 .
x2
(
λ x10 .
0
)
0
(
λ x10 .
0
)
(
λ x10 .
0
)
)
)
)
(
λ x9 .
x0
(
λ x10 .
x3
(
λ x11 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
x3
(
λ x12 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
0
)
0
0
(
λ x12 :
ι → ι
.
λ x13 .
0
)
0
0
)
(
Inj0
0
)
(
x2
(
λ x11 .
0
)
0
(
λ x11 .
0
)
(
λ x11 .
0
)
)
(
λ x11 :
ι → ι
.
λ x12 .
x10
)
(
x1
(
λ x11 x12 .
0
)
0
)
(
setsum
0
0
)
)
(
λ x10 :
(
ι → ι
)
→ ι
.
x10
(
λ x11 .
x2
(
λ x12 .
0
)
0
(
λ x12 .
0
)
(
λ x12 .
0
)
)
)
)
(
λ x9 .
x7
)
)
(
λ x9 :
ι → ι
.
λ x10 .
x2
(
λ x11 .
x11
)
(
setsum
(
x3
(
λ x11 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
Inj1
0
)
(
x3
(
λ x11 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
0
)
0
0
(
λ x11 :
ι → ι
.
λ x12 .
0
)
0
0
)
(
x2
(
λ x11 .
0
)
0
(
λ x11 .
0
)
(
λ x11 .
0
)
)
(
λ x11 :
ι → ι
.
λ x12 .
Inj0
0
)
x10
(
x9
0
)
)
(
setsum
(
x9
0
)
(
Inj1
0
)
)
)
(
λ x11 .
Inj0
(
Inj1
(
Inj0
0
)
)
)
(
λ x11 .
Inj1
(
setsum
(
Inj1
0
)
0
)
)
)
(
x2
(
setsum
(
setsum
0
(
x0
(
λ x9 .
0
)
(
λ x9 :
(
ι → ι
)
→ ι
.
0
)
)
)
)
(
Inj0
0
)
(
λ x9 .
x0
(
λ x10 .
setsum
(
x0
(
λ x11 .
0
)
(
λ x11 :
(
ι → ι
)
→ ι
.
0
)
)
0
)
(
λ x10 :
(
ι → ι
)
→ ι
.
0
)
)
(
λ x9 .
0
)
)
(
x0
(
λ x9 .
x3
(
λ x10 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
x0
(
λ x11 .
0
)
(
λ x11 :
(
ι → ι
)
→ ι
.
0
)
)
(
x0
(
λ x10 .
x2
(
λ x11 .
0
)
0
(
λ x11 .
0
)
(
λ x11 .
0
)
)
(
λ x10 :
(
ι → ι
)
→ ι
.
x2
(
λ x11 .
0
)
0
(
λ x11 .
0
)
(
λ x11 .
0
)
)
)
(
Inj1
x7
)
(
λ x10 :
ι → ι
.
λ x11 .
x0
(
λ x12 .
0
)
(
λ x12 :
(
ι → ι
)
→ ι
.
x12
(
λ x13 .
0
)
)
)
0
0
)
(
λ x9 :
(
ι → ι
)
→ ι
.
x3
(
λ x10 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
setsum
(
x1
(
λ x11 x12 .
0
)
0
)
(
x9
(
λ x11 .
0
)
)
)
0
0
(
λ x10 :
ι → ι
.
λ x11 .
x10
0
)
(
setsum
x6
(
Inj1
0
)
)
(
x9
(
λ x10 .
x9
(
λ x11 .
0
)
)
)
)
)
=
x0
(
λ x9 .
setsum
x5
(
setsum
0
x6
)
)
(
λ x9 :
(
ι → ι
)
→ ι
.
x9
(
λ x10 .
x1
(
λ x11 x12 .
Inj1
(
setsum
0
0
)
)
(
x2
(
λ x11 .
x3
(
λ x12 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
0
)
0
0
(
λ x12 :
ι → ι
.
λ x13 .
0
)
0
0
)
(
x9
(
λ x11 .
0
)
)
(
λ x11 .
x2
(
λ x12 .
0
)
0
(
λ x12 .
0
)
(
λ x12 .
0
)
)
(
λ x11 .
x10
)
)
)
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→ ι
.
∀ x5 .
∀ x6 :
ι → ι
.
∀ x7 .
x3
(
λ x9 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
Inj1
0
)
0
0
(
λ x9 :
ι → ι
.
λ x10 .
0
)
0
(
x4
(
λ x9 .
setsum
(
Inj1
(
x6
0
)
)
x5
)
)
=
setsum
0
(
x0
(
λ x9 .
x3
(
λ x10 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
x0
(
λ x11 .
0
)
(
λ x11 :
(
ι → ι
)
→ ι
.
x2
(
λ x12 .
0
)
0
(
λ x12 .
0
)
(
λ x12 .
0
)
)
)
(
Inj0
x9
)
(
setsum
0
(
setsum
0
0
)
)
(
λ x10 :
ι → ι
.
λ x11 .
setsum
0
(
Inj0
0
)
)
(
x1
(
λ x10 x11 .
x0
(
λ x12 .
0
)
(
λ x12 :
(
ι → ι
)
→ ι
.
0
)
)
0
)
(
Inj1
0
)
)
(
λ x9 :
(
ι → ι
)
→ ι
.
setsum
0
(
Inj0
x5
)
)
)
)
⟶
(
∀ x4 x5 :
ι → ι
.
∀ x6 :
(
ι →
(
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x7 .
x2
(
λ x9 .
0
)
0
(
λ x9 .
setsum
x7
(
x5
(
x3
(
λ x10 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
x10
(
λ x11 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x11 x12 .
0
)
)
(
x0
(
λ x10 .
0
)
(
λ x10 :
(
ι → ι
)
→ ι
.
0
)
)
(
x3
(
λ x10 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
0
)
0
0
(
λ x10 :
ι → ι
.
λ x11 .
0
)
0
0
)
(
λ x10 :
ι → ι
.
λ x11 .
0
)
(
Inj1
0
)
0
)
)
)
(
λ x9 .
Inj1
(
x6
(
λ x10 .
λ x11 :
ι → ι
.
x0
(
λ x12 .
setsum
0
0
)
(
λ x12 :
(
ι → ι
)
→ ι
.
x11
0
)
)
(
λ x10 :
ι → ι
.
setsum
(
x0
(
λ x11 .
0
)
(
λ x11 :
(
ι → ι
)
→ ι
.
0
)
)
(
x10
0
)
)
)
)
=
x4
0
)
⟶
(
∀ x4 .
∀ x5 :
(
ι → ι
)
→
ι →
(
ι → ι
)
→ ι
.
∀ x6 .
∀ x7 :
ι →
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
x2
(
λ x9 .
x3
(
λ x10 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
x7
(
x3
(
λ x11 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
x2
(
λ x12 .
0
)
0
(
λ x12 .
0
)
(
λ x12 .
0
)
)
0
(
setsum
0
0
)
(
λ x11 :
ι → ι
.
λ x12 .
0
)
x6
(
x3
(
λ x11 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
0
)
0
0
(
λ x11 :
ι → ι
.
λ x12 .
0
)
0
0
)
)
(
λ x11 :
ι → ι
.
0
)
(
λ x11 .
Inj1
(
Inj0
0
)
)
)
(
x5
(
λ x10 .
x9
)
(
x2
(
λ x10 .
Inj0
0
)
0
(
λ x10 .
x10
)
(
λ x10 .
x7
0
(
λ x11 :
ι → ι
.
0
)
(
λ x11 .
0
)
)
)
(
λ x10 .
x0
(
λ x11 .
x10
)
(
λ x11 :
(
ι → ι
)
→ ι
.
x7
0
(
λ x12 :
ι → ι
.
0
)
(
λ x12 .
0
)
)
)
)
(
x2
(
λ x10 .
setsum
(
Inj1
0
)
(
setsum
0
0
)
)
(
setsum
(
x0
(
λ x10 .
0
)
(
λ x10 :
(
ι → ι
)
→ ι
.
0
)
)
(
Inj0
0
)
)
(
λ x10 .
x10
)
(
λ x10 .
x10
)
)
(
λ x10 :
ι → ι
.
λ x11 .
Inj0
(
setsum
(
x3
(
λ x12 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
0
)
0
0
(
λ x12 :
ι → ι
.
λ x13 .
0
)
0
0
)
(
Inj1
0
)
)
)
0
(
x7
x9
(
λ x10 :
ι → ι
.
0
)
(
λ x10 .
x10
)
)
)
(
setsum
(
x0
(
λ x9 .
x2
(
λ x10 .
0
)
x9
(
λ x10 .
x6
)
(
λ x10 .
x6
)
)
(
λ x9 :
(
ι → ι
)
→ ι
.
setsum
(
x0
(
λ x10 .
0
)
(
λ x10 :
(
ι → ι
)
→ ι
.
0
)
)
0
)
)
0
)
(
λ x9 .
0
)
(
λ x9 .
0
)
=
Inj0
0
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 .
∀ x7 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
x1
(
λ x9 x10 .
0
)
(
x1
(
λ x9 x10 .
0
)
(
x1
(
λ x9 x10 .
x6
)
(
x3
(
λ x9 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
x6
)
0
0
(
λ x9 :
ι → ι
.
λ x10 .
Inj1
0
)
(
x3
(
λ x9 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
0
)
0
0
(
λ x9 :
ι → ι
.
λ x10 .
0
)
0
0
)
(
x7
0
0
(
λ x9 .
0
)
0
)
)
)
)
=
x1
(
λ x9 x10 .
x10
)
(
x7
(
x0
(
λ x9 .
x6
)
(
λ x9 :
(
ι → ι
)
→ ι
.
Inj1
(
x2
(
λ x10 .
0
)
0
(
λ x10 .
0
)
(
λ x10 .
0
)
)
)
)
(
x2
(
λ x9 .
x3
(
λ x10 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
Inj0
0
)
x6
0
(
λ x10 :
ι → ι
.
λ x11 .
x7
0
0
(
λ x12 .
0
)
0
)
(
x3
(
λ x10 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
0
)
0
0
(
λ x10 :
ι → ι
.
λ x11 .
0
)
0
0
)
0
)
(
x2
(
λ x9 .
Inj0
0
)
(
x5
0
)
(
λ x9 .
x3
(
λ x10 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
0
)
0
0
(
λ x10 :
ι → ι
.
λ x11 .
0
)
0
0
)
(
λ x9 .
0
)
)
(
λ x9 .
Inj0
(
x7
0
0
(
λ x10 .
0
)
0
)
)
(
λ x9 .
x3
(
λ x10 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
x7
0
0
(
λ x11 .
0
)
0
)
(
x0
(
λ x10 .
0
)
(
λ x10 :
(
ι → ι
)
→ ι
.
0
)
)
(
x0
(
λ x10 .
0
)
(
λ x10 :
(
ι → ι
)
→ ι
.
0
)
)
(
λ x10 :
ι → ι
.
λ x11 .
0
)
x6
(
setsum
0
0
)
)
)
(
λ x9 .
setsum
0
(
setsum
(
x5
0
)
(
x7
0
0
(
λ x10 .
0
)
0
)
)
)
0
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
.
∀ x7 :
ι → ι
.
x1
(
λ x9 x10 .
x7
(
setsum
(
x6
(
λ x11 :
(
ι → ι
)
→ ι
.
0
)
)
0
)
)
0
=
x7
(
Inj0
(
Inj1
(
setsum
(
x3
(
λ x9 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
0
)
0
0
(
λ x9 :
ι → ι
.
λ x10 .
0
)
0
0
)
(
x3
(
λ x9 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
0
)
0
0
(
λ x9 :
ι → ι
.
λ x10 .
0
)
0
0
)
)
)
)
)
⟶
(
∀ x4 :
ι →
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x5 :
ι → ι
.
∀ x6 x7 .
x0
(
λ x9 .
x3
(
λ x10 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
Inj0
0
)
(
x5
(
x3
(
λ x10 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
x9
)
(
setsum
0
0
)
0
(
λ x10 :
ι → ι
.
λ x11 .
setsum
0
0
)
(
Inj1
0
)
(
Inj1
0
)
)
)
0
(
λ x10 :
ι → ι
.
λ x11 .
0
)
(
Inj0
(
x3
(
λ x10 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
x0
(
λ x11 .
0
)
(
λ x11 :
(
ι → ι
)
→ ι
.
0
)
)
(
setsum
0
0
)
x6
(
λ x10 :
ι → ι
.
λ x11 .
x7
)
0
x7
)
)
(
setsum
(
x3
(
λ x10 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
0
)
(
x2
(
λ x10 .
0
)
0
(
λ x10 .
0
)
(
λ x10 .
0
)
)
(
x0
(
λ x10 .
0
)
(
λ x10 :
(
ι → ι
)
→ ι
.
0
)
)
(
λ x10 :
ι → ι
.
λ x11 .
0
)
x7
(
x0
(
λ x10 .
0
)
(
λ x10 :
(
ι → ι
)
→ ι
.
0
)
)
)
0
)
)
(
λ x9 :
(
ι → ι
)
→ ι
.
x9
(
λ x10 .
x0
(
λ x11 .
Inj0
0
)
(
λ x11 :
(
ι → ι
)
→ ι
.
Inj1
(
Inj0
0
)
)
)
)
=
x3
(
λ x9 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
setsum
0
x7
)
(
setsum
0
(
Inj0
x6
)
)
(
x2
(
λ x9 .
x6
)
0
(
λ x9 .
x3
(
λ x10 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
setsum
0
x9
)
(
setsum
(
x5
0
)
x6
)
(
x3
(
λ x10 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
x3
(
λ x11 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
0
)
0
0
(
λ x11 :
ι → ι
.
λ x12 .
0
)
0
0
)
0
(
Inj0
0
)
(
λ x10 :
ι → ι
.
λ x11 .
x7
)
(
x2
(
λ x10 .
0
)
0
(
λ x10 .
0
)
(
λ x10 .
0
)
)
0
)
(
λ x10 :
ι → ι
.
λ x11 .
Inj0
0
)
x7
x7
)
(
λ x9 .
x5
0
)
)
(
λ x9 :
ι → ι
.
λ x10 .
Inj0
(
x3
(
λ x11 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
0
)
0
x7
(
λ x11 :
ι → ι
.
λ x12 .
Inj0
0
)
(
x9
(
Inj0
0
)
)
x6
)
)
(
x3
(
λ x9 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
x5
x7
)
0
(
x5
(
setsum
(
setsum
0
0
)
(
Inj1
0
)
)
)
(
λ x9 :
ι → ι
.
λ x10 .
x2
(
λ x11 .
0
)
(
setsum
x6
x10
)
(
λ x11 .
x0
(
λ x12 .
Inj1
0
)
(
λ x12 :
(
ι → ι
)
→ ι
.
x12
(
λ x13 .
0
)
)
)
(
λ x11 .
0
)
)
(
x2
(
λ x9 .
x7
)
x7
(
λ x9 .
x3
(
λ x10 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
x3
(
λ x11 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
0
)
0
0
(
λ x11 :
ι → ι
.
λ x12 .
0
)
0
0
)
(
Inj0
0
)
(
x3
(
λ x10 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
0
)
0
0
(
λ x10 :
ι → ι
.
λ x11 .
0
)
0
0
)
(
λ x10 :
ι → ι
.
λ x11 .
0
)
(
x0
(
λ x10 .
0
)
(
λ x10 :
(
ι → ι
)
→ ι
.
0
)
)
x6
)
(
λ x9 .
x1
(
λ x10 x11 .
x2
(
λ x12 .
0
)
0
(
λ x12 .
0
)
(
λ x12 .
0
)
)
(
x0
(
λ x10 .
0
)
(
λ x10 :
(
ι → ι
)
→ ι
.
0
)
)
)
)
(
x0
(
λ x9 .
x6
)
(
λ x9 :
(
ι → ι
)
→ ι
.
setsum
(
x3
(
λ x10 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
0
)
0
0
(
λ x10 :
ι → ι
.
λ x11 .
0
)
0
0
)
0
)
)
)
(
Inj0
(
x1
(
λ x9 x10 .
x0
(
λ x11 .
x3
(
λ x12 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
.
0
)
0
0
(
λ x12 :
ι → ι
.
λ x13 .
0
)
0
0
)
(
λ x11 :
(
ι → ι
)
→ ι
.
setsum
0
0
)
)
0
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 x6 .
∀ x7 :
ι →
ι → ι
.
x0
(
λ x9 .
x5
)
(
λ x9 :
(
ι → ι
)
→ ι
.
0
)
=
setsum
x6
0
)
⟶
False
(proof)
Theorem
7afb6..
:
∀ x0 :
(
ι →
ι →
(
ι →
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→ ι
.
∀ x1 :
(
(
ι → ι
)
→
(
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
)
→
ι →
ι →
ι → ι
)
→
ι → ι
.
∀ x2 :
(
(
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→
ι → ι
.
∀ x3 :
(
(
ι →
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι →
ι → ι
.
(
∀ x4 :
ι → ι
.
∀ x5 x6 x7 .
x3
(
λ x9 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 .
0
)
(
λ x9 .
x7
)
(
Inj1
x6
)
0
=
setsum
(
x4
(
x4
x5
)
)
x7
)
⟶
(
∀ x4 :
ι →
ι →
ι →
ι → ι
.
∀ x5 :
(
ι → ι
)
→ ι
.
∀ x6 .
∀ x7 :
ι → ι
.
x3
(
λ x9 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 .
setsum
(
Inj1
(
x1
(
λ x11 :
ι → ι
.
λ x12 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
λ x13 x14 x15 .
Inj1
0
)
x10
)
)
0
)
(
λ x9 .
x9
)
(
x7
(
setsum
(
x4
(
x5
(
λ x9 .
0
)
)
(
x4
0
0
0
0
)
0
(
x5
(
λ x9 .
0
)
)
)
0
)
)
(
x3
(
λ x9 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 .
x3
(
λ x11 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x12 .
Inj0
(
setsum
0
0
)
)
(
λ x11 .
x10
)
(
x7
(
x1
(
λ x11 :
ι → ι
.
λ x12 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
λ x13 x14 x15 .
0
)
0
)
)
x10
)
(
λ x9 .
x9
)
(
x0
(
λ x9 x10 .
λ x11 :
ι →
ι → ι
.
x11
0
(
x3
(
λ x12 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x13 .
0
)
(
λ x12 .
0
)
0
0
)
)
(
x4
0
(
x0
(
λ x9 x10 .
λ x11 :
ι →
ι → ι
.
0
)
0
(
λ x9 .
0
)
)
(
x2
(
λ x9 :
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x10 .
0
)
0
)
0
)
(
λ x9 .
0
)
)
(
x2
(
λ x9 :
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x10 .
x10
)
(
setsum
x6
(
x2
(
λ x9 :
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x10 .
0
)
0
)
)
)
)
=
setsum
(
setsum
(
setsum
0
(
x3
(
λ x9 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 .
setsum
0
0
)
(
λ x9 .
x6
)
(
setsum
0
0
)
(
x7
0
)
)
)
(
x1
(
λ x9 :
ι → ι
.
λ x10 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
λ x11 x12 x13 .
x3
(
λ x14 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x15 .
x14
0
(
λ x16 :
ι → ι
.
0
)
)
(
λ x14 .
x1
(
λ x15 :
ι → ι
.
λ x16 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
λ x17 x18 x19 .
0
)
0
)
(
x3
(
λ x14 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x15 .
0
)
(
λ x14 .
0
)
0
0
)
(
x0
(
λ x14 x15 .
λ x16 :
ι →
ι → ι
.
0
)
0
(
λ x14 .
0
)
)
)
x6
)
)
x6
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
∀ x6 .
∀ x7 :
ι → ι
.
x2
(
λ x9 :
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x10 .
Inj1
(
x0
(
λ x11 x12 .
λ x13 :
ι →
ι → ι
.
Inj0
x10
)
(
x7
(
x2
(
λ x11 :
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x12 .
0
)
0
)
)
(
λ x11 .
x10
)
)
)
0
=
x7
0
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 .
∀ x7 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→
ι →
(
ι → ι
)
→ ι
.
x2
(
λ x9 :
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x10 .
x6
)
(
Inj1
(
Inj0
(
Inj1
0
)
)
)
=
x6
)
⟶
(
∀ x4 :
ι →
(
ι → ι
)
→ ι
.
∀ x5 :
ι → ι
.
∀ x6 x7 .
x1
(
λ x9 :
ι → ι
.
λ x10 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
λ x11 x12 x13 .
x11
)
(
setsum
(
x2
(
λ x9 :
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x10 .
setsum
(
Inj0
0
)
0
)
(
x2
(
λ x9 :
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x10 .
x2
(
λ x11 :
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x12 .
0
)
0
)
(
x1
(
λ x9 :
ι → ι
.
λ x10 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
λ x11 x12 x13 .
0
)
0
)
)
)
(
x4
0
(
λ x9 .
setsum
(
x0
(
λ x10 x11 .
λ x12 :
ι →
ι → ι
.
0
)
0
(
λ x10 .
0
)
)
(
setsum
0
0
)
)
)
)
=
x7
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
ι → ι
.
x1
(
λ x9 :
ι → ι
.
λ x10 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
λ x11 x12 x13 .
x11
)
0
=
x6
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
x0
(
λ x9 x10 .
λ x11 :
ι →
ι → ι
.
0
)
(
x2
(
λ x9 :
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x10 .
x0
(
λ x11 x12 .
λ x13 :
ι →
ι → ι
.
0
)
0
(
λ x11 .
0
)
)
0
)
(
λ x9 .
0
)
=
x2
(
λ x9 :
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x10 .
setsum
(
x7
(
λ x11 :
ι → ι
.
setsum
(
setsum
0
0
)
(
x11
0
)
)
x6
)
(
setsum
x10
(
setsum
(
x2
(
λ x11 :
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x12 .
0
)
0
)
0
)
)
)
x6
)
⟶
(
∀ x4 :
ι →
ι → ι
.
∀ x5 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x6 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
ι →
ι →
ι → ι
.
∀ x7 :
(
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→ ι
.
x0
(
λ x9 x10 .
λ x11 :
ι →
ι → ι
.
0
)
(
Inj1
(
x6
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 .
x9
)
(
x4
0
0
)
(
setsum
(
x2
(
λ x9 :
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x10 .
0
)
0
)
0
)
(
x0
(
λ x9 x10 .
λ x11 :
ι →
ι → ι
.
setsum
0
0
)
(
x4
0
0
)
(
λ x9 .
x3
(
λ x10 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 .
0
)
(
λ x10 .
0
)
0
0
)
)
)
)
(
λ x9 .
0
)
=
x6
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 .
Inj1
0
)
(
x1
(
λ x9 :
ι → ι
.
λ x10 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
λ x11 x12 x13 .
0
)
(
x3
(
λ x9 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 .
0
)
(
λ x9 .
Inj0
(
x1
(
λ x10 :
ι → ι
.
λ x11 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
λ x12 x13 x14 .
0
)
0
)
)
0
(
x0
(
λ x9 x10 .
λ x11 :
ι →
ι → ι
.
0
)
(
x3
(
λ x9 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 .
0
)
(
λ x9 .
0
)
0
0
)
(
λ x9 .
x7
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 .
0
)
)
)
)
)
0
(
setsum
(
x6
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 .
x7
(
λ x12 :
(
ι → ι
)
→
ι → ι
.
λ x13 .
x2
(
λ x14 :
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x15 .
0
)
0
)
)
(
x4
(
x2
(
λ x9 :
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x10 .
0
)
0
)
(
x1
(
λ x9 :
ι → ι
.
λ x10 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
λ x11 x12 x13 .
0
)
0
)
)
(
x5
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 :
ι → ι
.
λ x11 .
x3
(
λ x12 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x13 .
0
)
(
λ x12 .
0
)
0
0
)
)
(
x7
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 .
Inj1
0
)
)
)
(
setsum
(
setsum
0
(
x7
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 .
0
)
)
)
0
)
)
)
⟶
False
(proof)
Theorem
000be..
:
∀ x0 :
(
ι →
ι →
ι → ι
)
→
ι → ι
.
∀ x1 :
(
ι →
ι →
(
ι → ι
)
→
ι → ι
)
→
(
(
ι →
ι →
ι → ι
)
→
ι →
ι → ι
)
→
ι → ι
.
∀ x2 :
(
(
ι → ι
)
→
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
(
(
ι →
ι → ι
)
→ ι
)
→ ι
)
→
ι →
ι → ι
.
∀ x3 :
(
ι →
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι → ι
)
→
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι → ι
.
(
∀ x4 :
ι → ι
.
∀ x5 :
ι →
ι → ι
.
∀ x6 .
∀ x7 :
(
(
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
x3
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 .
x10
(
λ x12 :
ι → ι
.
0
)
)
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
0
)
(
Inj0
(
setsum
(
x0
(
λ x9 x10 x11 .
0
)
(
x4
0
)
)
0
)
)
=
setsum
(
x7
(
λ x9 :
ι → ι
.
Inj1
(
x0
(
λ x10 x11 x12 .
x11
)
(
setsum
0
0
)
)
)
(
λ x9 :
ι → ι
.
λ x10 .
x3
(
λ x11 .
λ x12 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x13 .
Inj0
(
setsum
0
0
)
)
(
λ x11 :
(
ι → ι
)
→
ι → ι
.
0
)
(
x0
(
λ x11 x12 x13 .
x11
)
0
)
)
(
λ x9 .
x7
(
λ x10 :
ι → ι
.
0
)
(
λ x10 :
ι → ι
.
λ x11 .
Inj0
(
Inj0
0
)
)
(
λ x10 .
x0
(
λ x11 x12 x13 .
setsum
0
0
)
0
)
0
)
(
x7
(
λ x9 :
ι → ι
.
0
)
(
λ x9 :
ι → ι
.
λ x10 .
x1
(
λ x11 x12 .
λ x13 :
ι → ι
.
λ x14 .
x13
0
)
(
λ x11 :
ι →
ι →
ι → ι
.
λ x12 x13 .
x2
(
λ x14 x15 x16 :
ι → ι
.
λ x17 .
0
)
(
λ x14 :
(
ι →
ι → ι
)
→ ι
.
0
)
0
0
)
0
)
(
λ x9 .
0
)
(
setsum
(
x7
(
λ x9 :
ι → ι
.
0
)
(
λ x9 :
ι → ι
.
λ x10 .
0
)
(
λ x9 .
0
)
0
)
(
setsum
0
0
)
)
)
)
0
)
⟶
(
∀ x4 :
(
ι → ι
)
→ ι
.
∀ x5 :
ι →
(
ι →
ι → ι
)
→
ι → ι
.
∀ x6 :
ι → ι
.
∀ x7 .
x3
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 .
setsum
(
x2
(
λ x12 x13 x14 :
ι → ι
.
λ x15 .
x13
0
)
(
λ x12 :
(
ι →
ι → ι
)
→ ι
.
x10
(
λ x13 :
ι → ι
.
x2
(
λ x14 x15 x16 :
ι → ι
.
λ x17 .
0
)
(
λ x14 :
(
ι →
ι → ι
)
→ ι
.
0
)
0
0
)
)
0
x7
)
(
setsum
x9
(
Inj1
0
)
)
)
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
setsum
(
Inj0
0
)
0
)
0
=
Inj1
(
x1
(
λ x9 x10 .
λ x11 :
ι → ι
.
λ x12 .
x0
(
λ x13 x14 x15 .
x2
(
λ x16 x17 x18 :
ι → ι
.
λ x19 .
0
)
(
λ x16 :
(
ι →
ι → ι
)
→ ι
.
x15
)
x12
0
)
(
Inj1
0
)
)
(
λ x9 :
ι →
ι →
ι → ι
.
λ x10 x11 .
x0
(
λ x12 x13 x14 .
setsum
(
x1
(
λ x15 x16 .
λ x17 :
ι → ι
.
λ x18 .
0
)
(
λ x15 :
ι →
ι →
ι → ι
.
λ x16 x17 .
0
)
0
)
x12
)
(
x1
(
λ x12 x13 .
λ x14 :
ι → ι
.
λ x15 .
setsum
0
0
)
(
λ x12 :
ι →
ι →
ι → ι
.
λ x13 x14 .
Inj1
0
)
x10
)
)
(
Inj0
(
setsum
(
x2
(
λ x9 x10 x11 :
ι → ι
.
λ x12 .
0
)
(
λ x9 :
(
ι →
ι → ι
)
→ ι
.
0
)
0
0
)
(
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
∀ x5 :
(
(
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x6 :
ι →
(
ι → ι
)
→ ι
.
∀ x7 :
ι → ι
.
x2
(
λ x9 x10 x11 :
ι → ι
.
λ x12 .
0
)
(
λ x9 :
(
ι →
ι → ι
)
→ ι
.
x7
(
setsum
(
x3
(
λ x10 .
λ x11 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x12 .
x9
(
λ x13 x14 .
0
)
)
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
x10
(
λ x11 .
0
)
0
)
0
)
(
x6
(
x7
0
)
(
λ x10 .
x6
0
(
λ x11 .
0
)
)
)
)
)
(
x7
(
Inj1
(
Inj0
(
setsum
0
0
)
)
)
)
(
setsum
0
(
x5
(
λ x9 x10 :
ι → ι
.
Inj1
(
x1
(
λ x11 x12 .
λ x13 :
ι → ι
.
λ x14 .
0
)
(
λ x11 :
ι →
ι →
ι → ι
.
λ x12 x13 .
0
)
0
)
)
(
λ x9 :
ι → ι
.
x9
(
x6
0
(
λ x10 .
0
)
)
)
)
)
=
x7
(
setsum
(
x2
(
λ x9 x10 x11 :
ι → ι
.
λ x12 .
setsum
(
x2
(
λ x13 x14 x15 :
ι → ι
.
λ x16 .
0
)
(
λ x13 :
(
ι →
ι → ι
)
→ ι
.
0
)
0
0
)
(
x11
0
)
)
(
λ x9 :
(
ι →
ι → ι
)
→ ι
.
x5
(
λ x10 x11 :
ι → ι
.
0
)
(
λ x10 :
ι → ι
.
setsum
0
0
)
)
(
x6
0
(
λ x9 .
0
)
)
0
)
(
setsum
0
(
x5
(
λ x9 x10 :
ι → ι
.
Inj0
0
)
(
λ x9 :
ι → ι
.
Inj1
0
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
ι → ι
.
∀ x6 x7 .
x2
(
λ x9 x10 x11 :
ι → ι
.
λ x12 .
setsum
(
Inj1
(
Inj0
0
)
)
(
setsum
0
(
setsum
(
x9
0
)
(
setsum
0
0
)
)
)
)
(
λ x9 :
(
ι →
ι → ι
)
→ ι
.
setsum
(
setsum
0
0
)
(
x2
(
λ x10 x11 x12 :
ι → ι
.
λ x13 .
x0
(
λ x14 x15 x16 .
x14
)
0
)
(
λ x10 :
(
ι →
ι → ι
)
→ ι
.
x9
(
λ x11 x12 .
x10
(
λ x13 x14 .
0
)
)
)
x6
0
)
)
(
Inj0
0
)
(
setsum
x7
x7
)
=
x4
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
(
ι → ι
)
→ ι
.
x1
(
λ x9 x10 .
λ x11 :
ι → ι
.
λ x12 .
x3
(
λ x13 .
λ x14 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x15 .
0
)
(
λ x13 :
(
ι → ι
)
→
ι → ι
.
x2
(
λ x14 x15 x16 :
ι → ι
.
λ x17 .
0
)
(
λ x14 :
(
ι →
ι → ι
)
→ ι
.
x3
(
λ x15 .
λ x16 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x17 .
x3
(
λ x18 .
λ x19 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x20 .
0
)
(
λ x18 :
(
ι → ι
)
→
ι → ι
.
0
)
0
)
(
λ x15 :
(
ι → ι
)
→
ι → ι
.
x1
(
λ x16 x17 .
λ x18 :
ι → ι
.
λ x19 .
0
)
(
λ x16 :
ι →
ι →
ι → ι
.
λ x17 x18 .
0
)
0
)
(
x14
(
λ x15 x16 .
0
)
)
)
(
setsum
(
x0
(
λ x14 x15 x16 .
0
)
0
)
(
x13
(
λ x14 .
0
)
0
)
)
(
setsum
(
setsum
0
0
)
(
x0
(
λ x14 x15 x16 .
0
)
0
)
)
)
(
Inj0
(
setsum
(
x2
(
λ x13 x14 x15 :
ι → ι
.
λ x16 .
0
)
(
λ x13 :
(
ι →
ι → ι
)
→ ι
.
0
)
0
0
)
0
)
)
)
(
λ x9 :
ι →
ι →
ι → ι
.
λ x10 x11 .
x10
)
(
x2
(
λ x9 x10 x11 :
ι → ι
.
λ x12 .
setsum
(
Inj0
(
setsum
0
0
)
)
0
)
(
λ x9 :
(
ι →
ι → ι
)
→ ι
.
x5
)
(
Inj1
0
)
0
)
=
x2
(
λ x9 x10 x11 :
ι → ι
.
λ x12 .
setsum
(
x9
(
x11
x12
)
)
0
)
(
λ x9 :
(
ι →
ι → ι
)
→ ι
.
setsum
(
setsum
(
x3
(
λ x10 .
λ x11 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x12 .
x9
(
λ x13 x14 .
0
)
)
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
x9
(
λ x11 x12 .
0
)
)
0
)
(
x7
(
λ x10 .
setsum
0
0
)
)
)
(
setsum
0
0
)
)
(
setsum
0
(
x7
(
λ x9 .
x6
)
)
)
x6
)
⟶
(
∀ x4 .
∀ x5 :
(
ι →
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x6 .
∀ x7 :
(
ι → ι
)
→ ι
.
x1
(
λ x9 x10 .
λ x11 :
ι → ι
.
setsum
(
x1
(
λ x12 x13 .
λ x14 :
ι → ι
.
λ x15 .
Inj0
x12
)
(
λ x12 :
ι →
ι →
ι → ι
.
λ x13 x14 .
0
)
(
Inj1
(
Inj1
0
)
)
)
)
(
λ x9 :
ι →
ι →
ι → ι
.
λ x10 x11 .
Inj1
(
x7
(
λ x12 .
0
)
)
)
0
=
x5
(
λ x9 x10 .
x2
(
λ x11 x12 x13 :
ι → ι
.
λ x14 .
x12
(
x2
(
λ x15 x16 x17 :
ι → ι
.
λ x18 .
x1
(
λ x19 x20 .
λ x21 :
ι → ι
.
λ x22 .
0
)
(
λ x19 :
ι →
ι →
ι → ι
.
λ x20 x21 .
0
)
0
)
(
λ x15 :
(
ι →
ι → ι
)
→ ι
.
Inj1
0
)
0
(
setsum
0
0
)
)
)
(
λ x11 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
Inj1
0
)
0
)
(
λ x9 :
ι → ι
.
λ x10 .
x3
(
λ x11 .
λ x12 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x13 .
x3
(
λ x14 .
λ x15 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x16 .
x16
)
(
λ x14 :
(
ι → ι
)
→
ι → ι
.
x12
(
λ x15 :
ι → ι
.
x3
(
λ x16 .
λ x17 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x18 .
0
)
(
λ x16 :
(
ι → ι
)
→
ι → ι
.
0
)
0
)
)
0
)
(
λ x11 :
(
ι → ι
)
→
ι → ι
.
0
)
(
Inj1
(
setsum
(
x1
(
λ x11 x12 .
λ x13 :
ι → ι
.
λ x14 .
0
)
(
λ x11 :
ι →
ι →
ι → ι
.
λ x12 x13 .
0
)
0
)
x10
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
∀ x6 x7 .
x0
(
λ x9 x10 x11 .
0
)
0
=
Inj0
(
setsum
(
x1
(
λ x9 x10 .
λ x11 :
ι → ι
.
λ x12 .
x10
)
(
λ x9 :
ι →
ι →
ι → ι
.
λ x10 x11 .
x7
)
0
)
0
)
)
⟶
(
∀ x4 .
∀ x5 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x6 x7 .
x0
(
λ x9 x10 x11 .
x2
(
λ x12 x13 x14 :
ι → ι
.
λ x15 .
0
)
(
λ x12 :
(
ι →
ι → ι
)
→ ι
.
Inj1
(
x0
(
λ x13 x14 x15 .
0
)
0
)
)
0
0
)
0
=
x2
(
λ x9 x10 x11 :
ι → ι
.
λ x12 .
x0
(
λ x13 x14 x15 .
x15
)
(
x11
(
setsum
(
x11
0
)
(
x10
0
)
)
)
)
(
λ x9 :
(
ι →
ι → ι
)
→ ι
.
setsum
(
setsum
0
(
Inj1
(
x9
(
λ x10 x11 .
0
)
)
)
)
(
x2
(
λ x10 x11 x12 :
ι → ι
.
λ x13 .
x3
(
λ x14 .
λ x15 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x16 .
Inj0
0
)
(
λ x14 :
(
ι → ι
)
→
ι → ι
.
x3
(
λ x15 .
λ x16 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x17 .
0
)
(
λ x15 :
(
ι → ι
)
→
ι → ι
.
0
)
0
)
(
setsum
0
0
)
)
(
λ x10 :
(
ι →
ι → ι
)
→ ι
.
x0
(
λ x11 x12 x13 .
x2
(
λ x14 x15 x16 :
ι → ι
.
λ x17 .
0
)
(
λ x14 :
(
ι →
ι → ι
)
→ ι
.
0
)
0
0
)
(
Inj1
0
)
)
(
x2
(
λ x10 x11 x12 :
ι → ι
.
λ x13 .
Inj1
0
)
(
λ x10 :
(
ι →
ι → ι
)
→ ι
.
x3
(
λ x11 .
λ x12 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x13 .
0
)
(
λ x11 :
(
ι → ι
)
→
ι → ι
.
0
)
0
)
(
setsum
0
0
)
(
x2
(
λ x10 x11 x12 :
ι → ι
.
λ x13 .
0
)
(
λ x10 :
(
ι →
ι → ι
)
→ ι
.
0
)
0
0
)
)
(
setsum
(
Inj1
0
)
(
x0
(
λ x10 x11 x12 .
0
)
0
)
)
)
)
x4
(
x2
(
λ x9 x10 x11 :
ι → ι
.
λ x12 .
x1
(
λ x13 x14 .
λ x15 :
ι → ι
.
λ x16 .
x14
)
(
λ x13 :
ι →
ι →
ι → ι
.
λ x14 x15 .
x12
)
x12
)
(
λ x9 :
(
ι →
ι → ι
)
→ ι
.
Inj1
(
setsum
(
setsum
0
0
)
0
)
)
0
(
x2
(
λ x9 x10 x11 :
ι → ι
.
λ x12 .
0
)
(
λ x9 :
(
ι →
ι → ι
)
→ ι
.
x3
(
λ x10 .
λ x11 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x12 .
Inj0
0
)
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
x10
(
λ x11 .
0
)
0
)
0
)
x4
0
)
)
)
⟶
False
(proof)
Theorem
ce3d6..
:
∀ x0 :
(
(
ι → ι
)
→ ι
)
→
ι →
(
(
ι →
ι → ι
)
→ ι
)
→ ι
.
∀ x1 :
(
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
)
→
ι → ι
.
∀ x2 :
(
ι →
ι →
ι →
(
ι → ι
)
→ ι
)
→
(
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι → ι
.
∀ x3 :
(
(
ι →
(
ι → ι
)
→ ι
)
→ ι
)
→
ι →
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
.
(
∀ x4 x5 x6 x7 .
x3
(
λ x9 :
ι →
(
ι → ι
)
→ ι
.
x9
x5
(
λ x10 .
0
)
)
0
(
λ x9 .
λ x10 :
ι → ι
.
x9
)
(
setsum
(
x0
(
λ x9 :
ι → ι
.
x9
(
Inj1
0
)
)
x4
(
λ x9 :
ι →
ι → ι
.
0
)
)
0
)
=
x4
)
⟶
(
∀ x4 :
ι →
ι →
(
ι → ι
)
→ ι
.
∀ x5 x6 x7 .
x3
(
λ x9 :
ι →
(
ι → ι
)
→ ι
.
0
)
(
Inj0
0
)
(
λ x9 .
λ x10 :
ι → ι
.
x3
(
λ x11 :
ι →
(
ι → ι
)
→ ι
.
setsum
0
(
x11
0
(
λ x12 .
0
)
)
)
x6
(
λ x11 .
λ x12 :
ι → ι
.
x1
(
λ x13 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
0
)
(
setsum
x9
(
x2
(
λ x11 x12 x13 .
λ x14 :
ι → ι
.
x12
)
(
λ x11 :
ι →
(
ι → ι
)
→
ι → ι
.
0
)
x6
)
)
)
(
x2
(
λ x9 x10 x11 .
λ x12 :
ι → ι
.
setsum
(
x0
(
λ x13 :
ι → ι
.
setsum
0
0
)
(
x0
(
λ x13 :
ι → ι
.
0
)
0
(
λ x13 :
ι →
ι → ι
.
0
)
)
(
λ x13 :
ι →
ι → ι
.
0
)
)
(
setsum
x11
(
x2
(
λ x13 x14 x15 .
λ x16 :
ι → ι
.
0
)
(
λ x13 :
ι →
(
ι → ι
)
→
ι → ι
.
0
)
0
)
)
)
(
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
0
)
x5
)
=
x2
(
λ x9 x10 x11 .
λ x12 :
ι → ι
.
setsum
x9
(
Inj0
x9
)
)
(
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
x5
)
x6
)
⟶
(
∀ x4 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
∀ x5 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x6 :
ι →
ι → ι
.
∀ x7 .
x2
(
λ x9 x10 x11 .
λ x12 :
ι → ι
.
x9
)
(
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
x6
(
x6
(
Inj0
(
x3
(
λ x10 :
ι →
(
ι → ι
)
→ ι
.
0
)
0
(
λ x10 .
λ x11 :
ι → ι
.
0
)
0
)
)
(
setsum
(
x1
(
λ x10 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
0
)
(
x9
0
(
λ x10 .
0
)
0
)
)
)
(
setsum
(
Inj1
(
x3
(
λ x10 :
ι →
(
ι → ι
)
→ ι
.
0
)
0
(
λ x10 .
λ x11 :
ι → ι
.
0
)
0
)
)
(
Inj0
(
x5
0
(
λ x10 :
ι → ι
.
λ x11 .
0
)
(
λ x10 .
0
)
0
)
)
)
)
0
=
setsum
(
setsum
0
(
x3
(
λ x9 :
ι →
(
ι → ι
)
→ ι
.
x5
0
(
λ x10 :
ι → ι
.
λ x11 .
setsum
0
0
)
(
λ x10 .
0
)
(
Inj0
0
)
)
(
x3
(
λ x9 :
ι →
(
ι → ι
)
→ ι
.
0
)
(
setsum
0
0
)
(
λ x9 .
λ x10 :
ι → ι
.
x3
(
λ x11 :
ι →
(
ι → ι
)
→ ι
.
0
)
0
(
λ x11 .
λ x12 :
ι → ι
.
0
)
0
)
(
setsum
0
0
)
)
(
λ x9 .
λ x10 :
ι → ι
.
0
)
(
Inj1
(
Inj1
0
)
)
)
)
0
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 :
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x7 :
ι → ι
.
x2
(
λ x9 x10 x11 .
λ x12 :
ι → ι
.
x2
(
λ x13 x14 x15 .
λ x16 :
ι → ι
.
x15
)
(
λ x13 :
ι →
(
ι → ι
)
→
ι → ι
.
x10
)
(
x0
(
λ x13 :
ι → ι
.
Inj1
0
)
(
x1
(
λ x13 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
x10
)
(
Inj0
0
)
)
(
λ x13 :
ι →
ι → ι
.
setsum
0
0
)
)
)
(
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
x0
(
λ x10 :
ι → ι
.
setsum
(
x7
(
setsum
0
0
)
)
0
)
(
setsum
0
0
)
(
λ x10 :
ι →
ι → ι
.
x1
(
λ x11 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
x9
(
x7
0
)
(
λ x12 .
0
)
(
x9
0
(
λ x12 .
0
)
0
)
)
(
x6
(
λ x11 :
ι → ι
.
0
)
)
)
)
0
=
x0
(
λ x9 :
ι → ι
.
x3
(
λ x10 :
ι →
(
ι → ι
)
→ ι
.
setsum
(
x7
0
)
(
x1
(
λ x11 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
x9
0
)
(
x2
(
λ x11 x12 x13 .
λ x14 :
ι → ι
.
0
)
(
λ x11 :
ι →
(
ι → ι
)
→
ι → ι
.
0
)
0
)
)
)
(
Inj1
(
x6
(
λ x10 :
ι → ι
.
x3
(
λ x11 :
ι →
(
ι → ι
)
→ ι
.
0
)
0
(
λ x11 .
λ x12 :
ι → ι
.
0
)
0
)
)
)
(
λ x10 .
λ x11 :
ι → ι
.
x9
(
x7
(
setsum
0
0
)
)
)
(
x9
(
x2
(
λ x10 x11 x12 .
λ x13 :
ι → ι
.
Inj0
0
)
(
λ x10 :
ι →
(
ι → ι
)
→
ι → ι
.
setsum
0
0
)
(
x3
(
λ x10 :
ι →
(
ι → ι
)
→ ι
.
0
)
0
(
λ x10 .
λ x11 :
ι → ι
.
0
)
0
)
)
)
)
(
setsum
0
(
x2
(
λ x9 x10 x11 .
λ x12 :
ι → ι
.
x11
)
(
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
Inj1
(
Inj0
0
)
)
(
x7
0
)
)
)
(
λ x9 :
ι →
ι → ι
.
x3
(
λ x10 :
ι →
(
ι → ι
)
→ ι
.
x2
(
λ x11 x12 x13 .
λ x14 :
ι → ι
.
setsum
(
x0
(
λ x15 :
ι → ι
.
0
)
0
(
λ x15 :
ι →
ι → ι
.
0
)
)
x13
)
(
λ x11 :
ι →
(
ι → ι
)
→
ι → ι
.
Inj0
(
x1
(
λ x12 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
0
)
)
(
x9
(
x3
(
λ x11 :
ι →
(
ι → ι
)
→ ι
.
0
)
0
(
λ x11 .
λ x12 :
ι → ι
.
0
)
0
)
0
)
)
(
x6
(
λ x10 :
ι → ι
.
setsum
(
setsum
0
0
)
(
x10
0
)
)
)
(
λ x10 .
λ x11 :
ι → ι
.
Inj0
(
x9
0
0
)
)
(
setsum
(
x5
(
x3
(
λ x10 :
ι →
(
ι → ι
)
→ ι
.
0
)
0
(
λ x10 .
λ x11 :
ι → ι
.
0
)
0
)
)
(
Inj0
(
x2
(
λ x10 x11 x12 .
λ x13 :
ι → ι
.
0
)
(
λ x10 :
ι →
(
ι → ι
)
→
ι → ι
.
0
)
0
)
)
)
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
.
∀ x5 :
ι →
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
∀ x6 x7 .
x1
(
λ x9 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
0
=
x6
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 .
∀ x7 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
x1
(
λ x9 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
x9
(
λ x10 :
ι → ι
.
λ x11 .
x2
(
λ x12 x13 x14 .
λ x15 :
ι → ι
.
Inj1
(
x15
0
)
)
(
λ x12 :
ι →
(
ι → ι
)
→
ι → ι
.
x11
)
(
Inj0
(
Inj0
0
)
)
)
)
(
x1
(
λ x9 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
x7
(
λ x10 .
x7
(
λ x11 .
setsum
0
0
)
(
λ x11 x12 .
setsum
0
0
)
(
λ x11 .
x11
)
)
(
λ x10 x11 .
x7
(
λ x12 .
x10
)
(
λ x12 x13 .
x13
)
(
λ x12 .
x11
)
)
(
λ x10 .
Inj0
(
x0
(
λ x11 :
ι → ι
.
0
)
0
(
λ x11 :
ι →
ι → ι
.
0
)
)
)
)
0
)
=
x1
(
λ x9 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
setsum
(
x3
(
λ x10 :
ι →
(
ι → ι
)
→ ι
.
x1
(
λ x11 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
x3
(
λ x12 :
ι →
(
ι → ι
)
→ ι
.
0
)
0
(
λ x12 .
λ x13 :
ι → ι
.
0
)
0
)
0
)
(
x0
(
λ x10 :
ι → ι
.
Inj0
0
)
x6
(
λ x10 :
ι →
ι → ι
.
x10
0
0
)
)
(
λ x10 .
λ x11 :
ι → ι
.
setsum
(
setsum
0
0
)
0
)
(
Inj0
(
x9
(
λ x10 :
ι → ι
.
λ x11 .
0
)
)
)
)
(
x5
x6
)
)
x4
)
⟶
(
∀ x4 x5 .
∀ x6 :
ι →
ι →
ι →
ι → ι
.
∀ x7 :
ι → ι
.
x0
(
λ x9 :
ι → ι
.
0
)
0
(
λ x9 :
ι →
ι → ι
.
0
)
=
Inj0
(
Inj1
(
x0
(
λ x9 :
ι → ι
.
x6
0
(
setsum
0
0
)
(
setsum
0
0
)
0
)
0
(
λ x9 :
ι →
ι → ι
.
x0
(
λ x10 :
ι → ι
.
x3
(
λ x11 :
ι →
(
ι → ι
)
→ ι
.
0
)
0
(
λ x11 .
λ x12 :
ι → ι
.
0
)
0
)
0
(
λ x10 :
ι →
ι → ι
.
x7
0
)
)
)
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
(
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x7 :
ι → ι
.
x0
(
λ x9 :
ι → ι
.
0
)
(
x0
(
λ x9 :
ι → ι
.
setsum
0
0
)
x5
(
λ x9 :
ι →
ι → ι
.
setsum
0
(
x7
0
)
)
)
(
λ x9 :
ι →
ι → ι
.
x5
)
=
Inj1
(
setsum
(
Inj1
(
x2
(
λ x9 x10 x11 .
λ x12 :
ι → ι
.
x10
)
(
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
0
)
0
)
)
x5
)
)
⟶
False
(proof)
Theorem
281bb..
:
∀ x0 :
(
ι →
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι →
ι →
ι → ι
.
∀ x1 :
(
(
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
)
→
(
ι →
ι →
(
ι → ι
)
→ ι
)
→ ι
.
∀ x2 :
(
ι →
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
∀ x3 :
(
(
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
)
→ ι
)
→
(
(
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
.
(
∀ x4 :
(
ι → ι
)
→ ι
.
∀ x5 :
ι → ι
.
∀ x6 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι →
ι → ι
.
∀ x7 :
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
)
→
ι →
ι →
ι → ι
.
x3
(
λ x9 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
.
x9
(
λ x10 .
λ x11 :
ι → ι
.
x11
(
x2
(
λ x12 .
λ x13 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x14 :
(
ι → ι
)
→ ι
.
λ x15 :
ι → ι
.
λ x16 .
Inj1
0
)
(
λ x12 .
λ x13 :
ι → ι
.
0
)
)
)
(
x7
(
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 :
ι → ι
.
Inj1
(
Inj0
0
)
)
(
x7
(
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 :
ι → ι
.
x1
(
λ x12 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
0
)
(
λ x12 x13 .
λ x14 :
ι → ι
.
0
)
)
(
x1
(
λ x10 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
0
)
(
λ x10 x11 .
λ x12 :
ι → ι
.
0
)
)
(
x3
(
λ x10 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
.
0
)
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 .
λ x12 :
ι → ι
.
λ x13 .
0
)
)
(
x2
(
λ x10 .
λ x11 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x12 :
(
ι → ι
)
→ ι
.
λ x13 :
ι → ι
.
λ x14 .
0
)
(
λ x10 .
λ x11 :
ι → ι
.
0
)
)
)
(
x7
(
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 :
ι → ι
.
0
)
(
x0
(
λ x10 x11 x12 x13 .
0
)
(
λ x10 :
ι → ι
.
0
)
0
0
0
)
(
x1
(
λ x10 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
0
)
(
λ x10 x11 .
λ x12 :
ι → ι
.
0
)
)
(
x9
(
λ x10 .
λ x11 :
ι → ι
.
0
)
0
)
)
0
)
)
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
λ x12 .
x12
)
=
x7
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
x3
(
λ x11 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
.
x10
(
setsum
(
x2
(
λ x12 .
λ x13 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x14 :
(
ι → ι
)
→ ι
.
λ x15 :
ι → ι
.
λ x16 .
0
)
(
λ x12 .
λ x13 :
ι → ι
.
0
)
)
(
setsum
0
0
)
)
)
(
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 .
λ x13 :
ι → ι
.
λ x14 .
Inj1
0
)
)
(
setsum
0
(
x3
(
λ x9 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
.
x7
(
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 :
ι → ι
.
setsum
0
0
)
(
Inj1
0
)
(
x3
(
λ x10 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
.
0
)
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 .
λ x12 :
ι → ι
.
λ x13 .
0
)
)
(
x9
(
λ x10 .
λ x11 :
ι → ι
.
0
)
0
)
)
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
λ x12 .
0
)
)
)
(
Inj0
(
x5
(
x4
(
λ x9 .
x5
0
)
)
)
)
(
x1
(
λ x9 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
x0
(
λ x10 x11 x12 x13 .
x1
(
λ x14 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
x1
(
λ x15 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
0
)
(
λ x15 x16 .
λ x17 :
ι → ι
.
0
)
)
(
λ x14 x15 .
λ x16 :
ι → ι
.
setsum
0
0
)
)
(
λ x10 :
ι → ι
.
x0
(
λ x11 x12 x13 x14 .
x2
(
λ x15 .
λ x16 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x17 :
(
ι → ι
)
→ ι
.
λ x18 :
ι → ι
.
λ x19 .
0
)
(
λ x15 .
λ x16 :
ι → ι
.
0
)
)
(
λ x11 :
ι → ι
.
x2
(
λ x12 .
λ x13 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x14 :
(
ι → ι
)
→ ι
.
λ x15 :
ι → ι
.
λ x16 .
0
)
(
λ x12 .
λ x13 :
ι → ι
.
0
)
)
(
Inj0
0
)
(
x10
0
)
0
)
(
x3
(
λ x10 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
.
Inj1
0
)
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 .
λ x12 :
ι → ι
.
λ x13 .
setsum
0
0
)
)
(
x1
(
λ x10 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
x6
(
λ x11 :
ι → ι
.
λ x12 .
0
)
0
0
0
)
(
λ x10 x11 .
λ x12 :
ι → ι
.
setsum
0
0
)
)
(
x0
(
λ x10 x11 x12 x13 .
0
)
(
λ x10 :
ι → ι
.
0
)
(
x1
(
λ x10 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
0
)
(
λ x10 x11 .
λ x12 :
ι → ι
.
0
)
)
(
x3
(
λ x10 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
.
0
)
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 .
λ x12 :
ι → ι
.
λ x13 .
0
)
)
(
x1
(
λ x10 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
0
)
(
λ x10 x11 .
λ x12 :
ι → ι
.
0
)
)
)
)
(
λ x9 x10 .
λ x11 :
ι → ι
.
0
)
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x6 .
∀ x7 :
(
(
ι → ι
)
→
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
x3
(
λ x9 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
.
x5
0
(
λ x10 :
ι → ι
.
λ x11 .
x3
(
λ x12 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
.
0
)
(
λ x12 :
(
ι → ι
)
→
ι → ι
.
λ x13 .
λ x14 :
ι → ι
.
λ x15 .
0
)
)
)
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
λ x12 .
x10
)
=
x5
x4
(
λ x9 :
ι → ι
.
λ x10 .
x2
(
λ x11 .
λ x12 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x13 :
(
ι → ι
)
→ ι
.
λ x14 :
ι → ι
.
λ x15 .
0
)
(
λ x11 .
λ x12 :
ι → ι
.
0
)
)
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 .
∀ x7 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
x2
(
λ x9 .
λ x10 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 :
ι → ι
.
λ x13 .
0
)
(
λ x9 .
λ x10 :
ι → ι
.
x10
0
)
=
x7
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 :
ι → ι
.
λ x11 .
0
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→ ι
.
∀ x5 .
∀ x6 :
(
(
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x7 :
ι →
ι →
ι → ι
.
x2
(
λ x9 .
λ x10 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 :
ι → ι
.
λ x13 .
0
)
(
λ x9 .
λ x10 :
ι → ι
.
0
)
=
Inj0
(
Inj1
(
x0
(
λ x9 x10 x11 x12 .
x1
(
λ x13 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
0
)
(
λ x13 x14 .
λ x15 :
ι → ι
.
0
)
)
(
λ x9 :
ι → ι
.
setsum
0
(
x3
(
λ x10 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
.
0
)
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 .
λ x12 :
ι → ι
.
λ x13 .
0
)
)
)
(
x7
(
x1
(
λ x9 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
0
)
(
λ x9 x10 .
λ x11 :
ι → ι
.
0
)
)
(
x7
0
0
0
)
(
setsum
0
0
)
)
(
setsum
(
x6
(
λ x9 :
ι → ι
.
0
)
(
λ x9 :
ι → ι
.
λ x10 .
0
)
(
λ x9 .
0
)
)
(
x7
0
0
0
)
)
(
x3
(
λ x9 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
.
Inj1
0
)
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
λ x12 .
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 x7 .
x1
(
λ x9 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
x3
(
λ x10 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
.
Inj1
(
Inj1
(
x2
(
λ x11 .
λ x12 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x13 :
(
ι → ι
)
→ ι
.
λ x14 :
ι → ι
.
λ x15 .
0
)
(
λ x11 .
λ x12 :
ι → ι
.
0
)
)
)
)
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 .
λ x12 :
ι → ι
.
λ x13 .
x10
(
λ x14 .
x14
)
(
setsum
0
(
x0
(
λ x14 x15 x16 x17 .
0
)
(
λ x14 :
ι → ι
.
0
)
0
0
0
)
)
)
)
(
λ x9 x10 .
λ x11 :
ι → ι
.
0
)
=
x3
(
λ x9 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
.
x3
(
λ x10 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
.
setsum
x7
(
x0
(
λ x11 x12 x13 x14 .
x1
(
λ x15 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
0
)
(
λ x15 x16 .
λ x17 :
ι → ι
.
0
)
)
(
λ x11 :
ι → ι
.
x9
(
λ x12 .
λ x13 :
ι → ι
.
0
)
0
)
(
Inj0
0
)
0
(
Inj1
0
)
)
)
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 .
λ x12 :
ι → ι
.
λ x13 .
x0
(
λ x14 x15 x16 x17 .
x17
)
(
λ x14 :
ι → ι
.
x14
0
)
0
(
x3
(
λ x14 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
.
0
)
(
λ x14 :
(
ι → ι
)
→
ι → ι
.
λ x15 .
λ x16 :
ι → ι
.
λ x17 .
x1
(
λ x18 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
0
)
(
λ x18 x19 .
λ x20 :
ι → ι
.
0
)
)
)
0
)
)
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
λ x12 .
x1
(
λ x13 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
Inj0
0
)
(
λ x13 x14 .
λ x15 :
ι → ι
.
setsum
x12
x13
)
)
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
x1
(
λ x9 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
setsum
(
x1
(
λ x10 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
setsum
(
setsum
0
0
)
(
x1
(
λ x11 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
0
)
(
λ x11 x12 .
λ x13 :
ι → ι
.
0
)
)
)
(
λ x10 x11 .
λ x12 :
ι → ι
.
x1
(
λ x13 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
0
)
(
λ x13 x14 .
λ x15 :
ι → ι
.
x0
(
λ x16 x17 x18 x19 .
0
)
(
λ x16 :
ι → ι
.
0
)
0
0
0
)
)
)
(
x3
(
λ x10 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
.
x6
)
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 .
λ x12 :
ι → ι
.
λ x13 .
x13
)
)
)
(
λ x9 x10 .
λ x11 :
ι → ι
.
0
)
=
x5
)
⟶
(
∀ x4 x5 :
ι →
ι →
ι →
ι → ι
.
∀ x6 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→
ι → ι
.
∀ x7 .
x0
(
λ x9 x10 x11 x12 .
setsum
0
x9
)
(
λ x9 :
ι → ι
.
x6
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
x0
(
λ x11 x12 x13 x14 .
x11
)
(
λ x11 :
ι → ι
.
Inj1
0
)
(
Inj1
(
setsum
0
0
)
)
0
0
)
(
λ x10 x11 .
x11
)
(
Inj0
(
x9
(
setsum
0
0
)
)
)
)
0
(
x0
(
λ x9 x10 x11 x12 .
x9
)
(
λ x9 :
ι → ι
.
x6
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x10 x11 .
0
)
(
Inj0
(
x2
(
λ x10 .
λ x11 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x12 :
(
ι → ι
)
→ ι
.
λ x13 :
ι → ι
.
λ x14 .
0
)
(
λ x10 .
λ x11 :
ι → ι
.
0
)
)
)
)
x7
(
setsum
x7
0
)
(
setsum
(
x6
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
x2
(
λ x10 .
λ x11 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x12 :
(
ι → ι
)
→ ι
.
λ x13 :
ι → ι
.
λ x14 .
0
)
(
λ x10 .
λ x11 :
ι → ι
.
0
)
)
(
λ x9 x10 .
Inj0
0
)
(
x6
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x9 x10 .
0
)
0
)
)
0
)
)
(
x4
(
Inj1
(
x3
(
λ x9 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
.
Inj0
0
)
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
λ x12 .
0
)
)
)
(
Inj0
(
x0
(
λ x9 x10 x11 x12 .
0
)
(
λ x9 :
ι → ι
.
x6
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x10 x11 .
0
)
0
)
(
Inj0
0
)
(
Inj0
0
)
0
)
)
(
x5
(
setsum
(
Inj0
0
)
(
setsum
0
0
)
)
(
x1
(
λ x9 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
0
)
(
λ x9 x10 .
λ x11 :
ι → ι
.
setsum
0
0
)
)
(
setsum
(
Inj1
0
)
x7
)
(
Inj1
0
)
)
(
setsum
(
x0
(
λ x9 x10 x11 x12 .
x10
)
(
λ x9 :
ι → ι
.
x3
(
λ x10 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
.
0
)
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 .
λ x12 :
ι → ι
.
λ x13 .
0
)
)
(
x0
(
λ x9 x10 x11 x12 .
0
)
(
λ x9 :
ι → ι
.
0
)
0
0
0
)
x7
(
x3
(
λ x9 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
.
0
)
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
λ x12 .
0
)
)
)
(
setsum
x7
0
)
)
)
=
x4
(
x0
(
λ x9 x10 x11 x12 .
Inj1
(
setsum
(
x2
(
λ x13 .
λ x14 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x15 :
(
ι → ι
)
→ ι
.
λ x16 :
ι → ι
.
λ x17 .
0
)
(
λ x13 .
λ x14 :
ι → ι
.
0
)
)
x9
)
)
(
λ x9 :
ι → ι
.
x0
(
λ x10 x11 x12 x13 .
0
)
(
λ x10 :
ι → ι
.
x6
(
λ x11 :
(
ι → ι
)
→
ι → ι
.
x3
(
λ x12 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
.
0
)
(
λ x12 :
(
ι → ι
)
→
ι → ι
.
λ x13 .
λ x14 :
ι → ι
.
λ x15 .
0
)
)
(
λ x11 x12 .
x1
(
λ x13 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
0
)
(
λ x13 x14 .
λ x15 :
ι → ι
.
0
)
)
(
x3
(
λ x11 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
.
0
)
(
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 .
λ x13 :
ι → ι
.
λ x14 .
0
)
)
)
(
x6
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
x3
(
λ x11 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
.
0
)
(
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 .
λ x13 :
ι → ι
.
λ x14 .
0
)
)
(
λ x10 x11 .
x2
(
λ x12 .
λ x13 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x14 :
(
ι → ι
)
→ ι
.
λ x15 :
ι → ι
.
λ x16 .
0
)
(
λ x12 .
λ x13 :
ι → ι
.
0
)
)
(
Inj0
0
)
)
(
x2
(
λ x10 .
λ x11 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x12 :
(
ι → ι
)
→ ι
.
λ x13 :
ι → ι
.
λ x14 .
0
)
(
λ x10 .
λ x11 :
ι → ι
.
x0
(
λ x12 x13 x14 x15 .
0
)
(
λ x12 :
ι → ι
.
0
)
0
0
0
)
)
0
)
(
x1
(
λ x9 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
0
)
(
λ x9 x10 .
λ x11 :
ι → ι
.
x11
(
Inj0
0
)
)
)
(
x4
(
Inj1
(
x2
(
λ x9 .
λ x10 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 :
ι → ι
.
λ x13 .
0
)
(
λ x9 .
λ x10 :
ι → ι
.
0
)
)
)
(
x4
(
x3
(
λ x9 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
.
0
)
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
λ x12 .
0
)
)
(
Inj0
0
)
(
Inj1
0
)
(
setsum
0
0
)
)
(
setsum
(
setsum
0
0
)
(
x1
(
λ x9 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
0
)
(
λ x9 x10 .
λ x11 :
ι → ι
.
0
)
)
)
(
x2
(
λ x9 .
λ x10 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 :
ι → ι
.
λ x13 .
setsum
0
0
)
(
λ x9 .
λ x10 :
ι → ι
.
setsum
0
0
)
)
)
0
)
(
setsum
(
x4
x7
(
x6
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
x9
(
λ x10 .
0
)
0
)
(
λ x9 x10 .
setsum
0
0
)
(
x5
0
0
0
0
)
)
(
x3
(
λ x9 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
.
x0
(
λ x10 x11 x12 x13 .
0
)
(
λ x10 :
ι → ι
.
0
)
0
0
0
)
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
λ x12 .
x10
)
)
(
Inj0
0
)
)
(
Inj0
0
)
)
(
x4
(
x6
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x9 x10 .
0
)
0
)
0
(
x4
(
setsum
(
x5
0
0
0
0
)
(
x1
(
λ x9 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
0
)
(
λ x9 x10 .
λ x11 :
ι → ι
.
0
)
)
)
(
x4
(
x3
(
λ x9 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
.
0
)
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
λ x12 .
0
)
)
(
x6
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x9 x10 .
0
)
0
)
(
setsum
0
0
)
0
)
0
x7
)
(
Inj0
(
x1
(
λ x9 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
x2
(
λ x10 .
λ x11 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x12 :
(
ι → ι
)
→ ι
.
λ x13 :
ι → ι
.
λ x14 .
0
)
(
λ x10 .
λ x11 :
ι → ι
.
0
)
)
(
λ x9 x10 .
λ x11 :
ι → ι
.
setsum
0
0
)
)
)
)
(
x2
(
λ x9 .
λ x10 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 :
ι → ι
.
λ x13 .
x12
(
x2
(
λ x14 .
λ x15 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x16 :
(
ι → ι
)
→ ι
.
λ x17 :
ι → ι
.
λ x18 .
0
)
(
λ x14 .
λ x15 :
ι → ι
.
x1
(
λ x16 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
0
)
(
λ x16 x17 .
λ x18 :
ι → ι
.
0
)
)
)
)
(
λ x9 .
λ x10 :
ι → ι
.
x1
(
λ x11 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
x10
x7
)
(
λ x11 x12 .
λ x13 :
ι → ι
.
0
)
)
)
)
⟶
(
∀ x4 :
(
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x5 x6 .
∀ x7 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→ ι
.
x0
(
λ x9 x10 x11 x12 .
0
)
(
λ x9 :
ι → ι
.
setsum
(
x9
(
x7
(
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 .
0
)
)
)
(
Inj1
(
x9
0
)
)
)
0
(
x4
(
λ x9 :
ι →
ι → ι
.
λ x10 x11 .
0
)
(
λ x9 .
x7
(
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 .
0
)
)
(
λ x9 .
0
)
x6
)
(
x1
(
λ x9 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
Inj0
(
setsum
0
(
x7
(
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 .
0
)
)
)
)
(
λ x9 x10 .
λ x11 :
ι → ι
.
x7
(
λ x12 :
(
ι → ι
)
→ ι
.
λ x13 .
x1
(
λ x14 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
x11
0
)
(
λ x14 x15 .
λ x16 :
ι → ι
.
0
)
)
)
)
=
x1
(
λ x9 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
x1
(
λ x10 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
x0
(
λ x11 x12 x13 x14 .
x1
(
λ x15 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
x2
(
λ x16 .
λ x17 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x18 :
(
ι → ι
)
→ ι
.
λ x19 :
ι → ι
.
λ x20 .
0
)
(
λ x16 .
λ x17 :
ι → ι
.
0
)
)
(
λ x15 x16 .
λ x17 :
ι → ι
.
0
)
)
(
λ x11 :
ι → ι
.
x11
(
Inj1
0
)
)
(
x9
(
λ x11 :
ι →
ι → ι
.
λ x12 :
ι → ι
.
x12
0
)
)
(
x3
(
λ x11 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
.
x3
(
λ x12 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
.
0
)
(
λ x12 :
(
ι → ι
)
→
ι → ι
.
λ x13 .
λ x14 :
ι → ι
.
λ x15 .
0
)
)
(
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 .
λ x13 :
ι → ι
.
λ x14 .
x2
(
λ x15 .
λ x16 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x17 :
(
ι → ι
)
→ ι
.
λ x18 :
ι → ι
.
λ x19 .
0
)
(
λ x15 .
λ x16 :
ι → ι
.
0
)
)
)
(
x1
(
λ x11 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
x9
(
λ x12 :
ι →
ι → ι
.
λ x13 :
ι → ι
.
0
)
)
(
λ x11 x12 .
λ x13 :
ι → ι
.
0
)
)
)
(
λ x10 x11 .
λ x12 :
ι → ι
.
0
)
)
(
λ x9 x10 .
λ x11 :
ι → ι
.
x1
(
λ x12 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
0
)
(
λ x12 x13 .
λ x14 :
ι → ι
.
0
)
)
)
⟶
False
(proof)
Theorem
ff51f..
:
∀ x0 :
(
ι → ι
)
→
ι → ι
.
∀ x1 :
(
ι → ι
)
→
(
ι → ι
)
→
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x2 :
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
∀ x3 :
(
(
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
)
→
ι → ι
.
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 .
∀ x7 :
(
ι →
ι →
ι → ι
)
→ ι
.
x3
(
λ x9 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
x7
(
λ x10 x11 x12 .
0
)
)
0
=
Inj1
(
x1
(
λ x9 .
x3
(
λ x10 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
(
x0
(
λ x10 .
Inj0
0
)
(
x0
(
λ x10 .
0
)
0
)
)
)
(
λ x9 .
setsum
(
x1
(
λ x10 .
Inj0
0
)
(
λ x10 .
Inj1
0
)
x6
(
λ x10 :
ι → ι
.
λ x11 .
0
)
)
(
x7
(
λ x10 x11 x12 .
setsum
0
0
)
)
)
x4
(
λ x9 :
ι → ι
.
λ x10 .
x2
(
λ x11 :
ι → ι
.
x2
(
λ x12 :
ι → ι
.
0
)
(
Inj0
0
)
)
(
x3
(
λ x11 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
x1
(
λ x12 .
0
)
(
λ x12 .
0
)
0
(
λ x12 :
ι → ι
.
λ x13 .
0
)
)
(
Inj0
0
)
)
)
)
)
⟶
(
∀ x4 :
ι →
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
∀ x5 .
∀ x6 :
(
ι →
ι → ι
)
→
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x7 :
(
ι →
ι →
ι → ι
)
→ ι
.
x3
(
λ x9 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
x2
(
λ x10 :
ι → ι
.
Inj1
(
setsum
0
(
x2
(
λ x11 :
ι → ι
.
0
)
0
)
)
)
(
x7
(
λ x10 x11 x12 .
x9
x10
(
λ x13 :
ι → ι
.
λ x14 .
setsum
0
0
)
)
)
)
(
x1
(
λ x9 .
x3
(
λ x10 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
(
x2
(
λ x10 :
ι → ι
.
0
)
(
Inj0
0
)
)
)
(
λ x9 .
0
)
x5
(
λ x9 :
ι → ι
.
λ x10 .
x2
(
λ x11 :
ι → ι
.
x9
(
x7
(
λ x12 x13 x14 .
0
)
)
)
(
x2
(
λ x11 :
ι → ι
.
x1
(
λ x12 .
0
)
(
λ x12 .
0
)
0
(
λ x12 :
ι → ι
.
λ x13 .
0
)
)
0
)
)
)
=
x2
(
λ x9 :
ι → ι
.
x2
(
λ x10 :
ι → ι
.
x2
(
λ x11 :
ι → ι
.
x0
(
λ x12 .
x10
0
)
(
setsum
0
0
)
)
0
)
(
setsum
(
x6
(
λ x10 x11 .
setsum
0
0
)
(
λ x10 x11 .
0
)
(
λ x10 .
x10
)
(
x6
(
λ x10 x11 .
0
)
(
λ x10 x11 .
0
)
(
λ x10 .
0
)
0
)
)
(
x2
(
λ x10 :
ι → ι
.
x9
0
)
(
x9
0
)
)
)
)
(
setsum
0
(
x6
(
λ x9 x10 .
0
)
(
λ x9 x10 .
Inj1
(
x3
(
λ x11 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
0
)
)
(
λ x9 .
Inj0
(
Inj0
0
)
)
(
Inj0
(
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 :
ι →
ι → ι
.
∀ x5 .
∀ x6 :
(
ι →
ι → ι
)
→
ι → ι
.
∀ x7 .
x2
(
λ x9 :
ι → ι
.
Inj1
(
x2
(
λ x10 :
ι → ι
.
x3
(
λ x11 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
x1
(
λ x12 .
0
)
(
λ x12 .
0
)
0
(
λ x12 :
ι → ι
.
λ x13 .
0
)
)
(
x10
0
)
)
(
x9
0
)
)
)
(
x0
(
λ x9 .
0
)
0
)
=
x0
(
λ x9 .
setsum
(
x0
(
λ x10 .
Inj0
(
setsum
0
0
)
)
(
Inj1
(
setsum
0
0
)
)
)
x5
)
x5
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x5 :
(
ι →
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
∀ x6 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
.
∀ x7 .
x2
(
λ x9 :
ι → ι
.
setsum
x7
(
Inj0
(
x5
(
λ x10 x11 .
0
)
(
x3
(
λ x10 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
0
)
(
λ x10 .
0
)
0
)
)
)
(
x3
(
λ x9 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
(
x5
(
λ x9 x10 .
x2
(
λ x11 :
ι → ι
.
x9
)
(
Inj0
0
)
)
(
setsum
(
x3
(
λ x9 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
0
)
(
x2
(
λ x9 :
ι → ι
.
0
)
0
)
)
(
λ x9 .
0
)
(
x4
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 .
x10
)
(
λ x9 :
ι → ι
.
λ x10 .
x0
(
λ x11 .
0
)
0
)
(
λ x9 .
setsum
0
0
)
(
Inj1
0
)
)
)
)
=
Inj0
(
x3
(
λ x9 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
x2
(
λ x10 :
ι → ι
.
x0
(
λ x11 .
0
)
(
x1
(
λ x11 .
0
)
(
λ x11 .
0
)
0
(
λ x11 :
ι → ι
.
λ x12 .
0
)
)
)
0
)
(
x6
(
λ x9 :
(
ι → ι
)
→ ι
.
0
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
∀ x6 :
ι →
(
ι → ι
)
→
ι → ι
.
∀ x7 .
x1
(
λ x9 .
0
)
(
λ x9 .
x9
)
(
x2
(
λ x9 :
ι → ι
.
x0
(
λ x10 .
x9
(
x2
(
λ x11 :
ι → ι
.
0
)
0
)
)
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
(
x2
(
λ x9 :
ι → ι
.
x6
(
Inj0
0
)
(
λ x10 .
x2
(
λ x11 :
ι → ι
.
0
)
0
)
(
Inj0
0
)
)
(
setsum
0
(
x0
(
λ x9 .
0
)
0
)
)
)
)
(
λ x9 :
ι → ι
.
λ x10 .
0
)
=
x2
(
λ x9 :
ι → ι
.
setsum
(
setsum
0
(
Inj1
0
)
)
(
x1
(
λ x10 .
0
)
(
λ x10 .
x7
)
0
(
λ x10 :
ι → ι
.
λ x11 .
setsum
0
(
x10
0
)
)
)
)
(
x0
(
λ x9 .
setsum
x9
0
)
x4
)
)
⟶
(
∀ x4 :
(
(
ι →
ι → ι
)
→ ι
)
→ ι
.
∀ x5 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x6 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
.
∀ x7 :
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι →
ι → ι
.
x1
(
λ x9 .
x6
(
λ x10 :
(
ι → ι
)
→ ι
.
x0
(
λ x11 .
x0
(
λ x12 .
0
)
(
x0
(
λ x12 .
0
)
0
)
)
(
setsum
0
0
)
)
)
(
λ x9 .
0
)
0
(
λ x9 :
ι → ι
.
λ x10 .
x0
(
λ x11 .
0
)
(
x1
(
λ x11 .
0
)
(
λ x11 .
0
)
(
setsum
(
x1
(
λ x11 .
0
)
(
λ x11 .
0
)
0
(
λ x11 :
ι → ι
.
λ x12 .
0
)
)
(
Inj1
0
)
)
(
λ x11 :
ι → ι
.
λ x12 .
x0
(
λ x13 .
0
)
x10
)
)
)
=
x0
(
λ x9 .
setsum
(
Inj1
(
setsum
0
(
setsum
0
0
)
)
)
(
x1
Inj1
(
λ x10 .
setsum
0
(
x1
(
λ x11 .
0
)
(
λ x11 .
0
)
0
(
λ x11 :
ι → ι
.
λ x12 .
0
)
)
)
(
x0
(
λ x10 .
x10
)
(
Inj1
0
)
)
(
λ x10 :
ι → ι
.
λ x11 .
x3
(
λ x12 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
setsum
0
0
)
(
x2
(
λ x12 :
ι → ι
.
0
)
0
)
)
)
)
(
x5
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 :
ι → ι
.
λ x11 .
0
)
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x5 .
∀ x6 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x7 .
x0
(
λ x9 .
0
)
(
Inj0
(
x4
(
λ x9 .
Inj0
0
)
(
λ x9 .
0
)
)
)
=
x5
)
⟶
(
∀ x4 :
(
ι →
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
∀ x5 :
ι → ι
.
∀ x6 .
∀ x7 :
ι → ι
.
x0
(
λ x9 .
x1
(
λ x10 .
x6
)
(
x0
(
λ x10 .
x1
(
λ x11 .
Inj0
0
)
(
λ x11 .
0
)
(
x0
(
λ x11 .
0
)
0
)
(
λ x11 :
ι → ι
.
λ x12 .
x1
(
λ x13 .
0
)
(
λ x13 .
0
)
0
(
λ x13 :
ι → ι
.
λ x14 .
0
)
)
)
)
(
Inj1
(
setsum
0
(
x5
0
)
)
)
(
λ x10 :
ι → ι
.
λ x11 .
x1
(
λ x12 .
setsum
(
x10
0
)
(
x1
(
λ x13 .
0
)
(
λ x13 .
0
)
0
(
λ x13 :
ι → ι
.
λ x14 .
0
)
)
)
(
λ x12 .
x3
(
λ x13 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
x13
0
(
λ x14 :
ι → ι
.
λ x15 .
0
)
)
0
)
(
x2
(
λ x12 :
ι → ι
.
x12
0
)
(
x7
0
)
)
(
λ x12 :
ι → ι
.
λ x13 .
0
)
)
)
(
x5
(
Inj1
0
)
)
=
x5
(
x1
(
λ x9 .
x5
(
x3
(
λ x10 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
Inj1
0
)
(
x5
0
)
)
)
(
λ x9 .
x7
0
)
0
(
λ x9 :
ι → ι
.
λ x10 .
x9
0
)
)
)
⟶
False
(proof)
Theorem
3f800..
:
∀ x0 :
(
(
ι →
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→ ι
.
∀ x1 :
(
ι →
(
(
ι →
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι → ι
.
∀ x2 :
(
ι → ι
)
→
ι → ι
.
∀ x3 :
(
ι → ι
)
→
ι →
ι → ι
.
(
∀ x4 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
.
∀ x5 x6 .
∀ x7 :
(
(
ι →
ι → ι
)
→
ι → ι
)
→
ι → ι
.
x3
(
λ x9 .
x7
(
λ x10 :
ι →
ι → ι
.
λ x11 .
0
)
(
x3
(
λ x10 .
x6
)
x9
(
Inj1
0
)
)
)
(
x2
(
λ x9 .
x3
(
λ x10 .
0
)
(
setsum
(
x3
(
λ x10 .
0
)
0
0
)
0
)
(
x3
(
λ x10 .
x2
(
λ x11 .
0
)
0
)
x5
(
x2
(
λ x10 .
0
)
0
)
)
)
(
x4
(
λ x9 :
(
ι → ι
)
→ ι
.
x9
(
λ x10 .
x0
(
λ x11 :
ι →
ι → ι
.
0
)
0
(
λ x11 .
0
)
)
)
)
)
x6
=
setsum
0
(
x4
(
λ x9 :
(
ι → ι
)
→ ι
.
Inj1
x6
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
.
∀ x6 .
∀ x7 :
ι → ι
.
x3
(
λ x9 .
setsum
x9
x9
)
(
x4
(
x5
(
λ x9 :
(
ι → ι
)
→ ι
.
0
)
)
)
(
Inj0
(
x2
(
λ x9 .
x1
(
λ x10 .
λ x11 :
(
ι →
ι → ι
)
→
ι → ι
.
λ x12 .
setsum
0
0
)
(
λ x10 :
ι → ι
.
x9
)
(
λ x10 :
(
ι → ι
)
→ ι
.
x6
)
(
setsum
0
0
)
)
(
x1
(
λ x9 .
λ x10 :
(
ι →
ι → ι
)
→
ι → ι
.
λ x11 .
setsum
0
0
)
(
λ x9 :
ι → ι
.
x3
(
λ x10 .
0
)
0
0
)
(
λ x9 :
(
ι → ι
)
→ ι
.
x2
(
λ x10 .
0
)
0
)
0
)
)
)
=
x4
(
x7
0
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x5 :
ι →
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
∀ x6 x7 :
ι → ι
.
x2
(
λ x9 .
x2
(
λ x10 .
x9
)
0
)
(
x2
(
λ x9 .
0
)
(
x5
(
Inj0
(
x2
(
λ x9 .
0
)
0
)
)
(
λ x9 :
ι → ι
.
x7
(
x3
(
λ x10 .
0
)
0
0
)
)
(
λ x9 .
x3
(
λ x10 .
0
)
(
x6
0
)
0
)
)
)
=
x2
(
λ x9 .
Inj0
(
setsum
x9
(
setsum
x9
0
)
)
)
(
setsum
0
(
x4
(
λ x9 .
x3
(
λ x10 .
Inj0
0
)
(
x5
0
(
λ x10 :
ι → ι
.
0
)
(
λ x10 .
0
)
)
(
x7
0
)
)
(
λ x9 .
x3
(
λ x10 .
0
)
(
x5
0
(
λ x10 :
ι → ι
.
0
)
(
λ x10 .
0
)
)
(
x0
(
λ x10 :
ι →
ι → ι
.
0
)
0
(
λ x10 .
0
)
)
)
)
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
(
ι → ι
)
→ ι
.
∀ x7 :
ι →
ι →
ι → ι
.
x2
(
λ x9 .
0
)
0
=
x5
)
⟶
(
∀ x4 :
(
ι →
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
∀ x5 :
(
(
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→ ι
.
∀ x6 .
∀ x7 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
.
x1
(
λ x9 .
λ x10 :
(
ι →
ι → ι
)
→
ι → ι
.
λ x11 .
x10
(
λ x12 x13 .
setsum
(
x0
(
λ x14 :
ι →
ι → ι
.
Inj0
0
)
x12
(
λ x14 .
x3
(
λ x15 .
0
)
0
0
)
)
(
x3
(
λ x14 .
x12
)
(
setsum
0
0
)
(
x10
(
λ x14 x15 .
0
)
0
)
)
)
0
)
(
λ x9 :
ι → ι
.
0
)
(
λ x9 :
(
ι → ι
)
→ ι
.
x5
(
λ x10 :
ι → ι
.
0
)
(
x0
(
λ x10 :
ι →
ι → ι
.
0
)
(
setsum
0
(
x7
(
λ x10 .
λ x11 :
ι → ι
.
λ x12 .
0
)
)
)
(
λ x10 .
x9
(
λ x11 .
0
)
)
)
(
λ x10 .
x10
)
)
(
setsum
(
x7
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 .
x11
)
)
0
)
=
Inj0
(
Inj1
(
x5
(
λ x9 :
ι → ι
.
x3
(
λ x10 .
0
)
(
x2
(
λ x10 .
0
)
0
)
(
x0
(
λ x10 :
ι →
ι → ι
.
0
)
0
(
λ x10 .
0
)
)
)
(
Inj0
(
x4
(
λ x9 x10 .
0
)
(
λ x9 x10 .
0
)
)
)
(
λ x9 .
x1
(
λ x10 .
λ x11 :
(
ι →
ι → ι
)
→
ι → ι
.
λ x12 .
Inj1
0
)
(
λ x10 :
ι → ι
.
setsum
0
0
)
(
λ x10 :
(
ι → ι
)
→ ι
.
Inj0
0
)
0
)
)
)
)
⟶
(
∀ x4 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
∀ x5 .
∀ x6 :
(
ι → ι
)
→ ι
.
∀ x7 :
(
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
x1
(
λ x9 .
λ x10 :
(
ι →
ι → ι
)
→
ι → ι
.
λ x11 .
x2
(
λ x12 .
Inj0
0
)
x9
)
(
λ x9 :
ι → ι
.
x0
(
λ x10 :
ι →
ι → ι
.
setsum
0
(
setsum
(
x2
(
λ x11 .
0
)
0
)
0
)
)
0
(
λ x10 .
Inj0
(
setsum
(
Inj0
0
)
0
)
)
)
(
λ x9 :
(
ι → ι
)
→ ι
.
0
)
(
x3
(
x2
(
λ x9 .
x9
)
)
(
x2
(
λ x9 .
x6
(
λ x10 .
x0
(
λ x11 :
ι →
ι → ι
.
0
)
0
(
λ x11 .
0
)
)
)
(
x7
(
λ x9 .
0
)
0
(
λ x9 .
x1
(
λ x10 .
λ x11 :
(
ι →
ι → ι
)
→
ι → ι
.
λ x12 .
0
)
(
λ x10 :
ι → ι
.
0
)
(
λ x10 :
(
ι → ι
)
→ ι
.
0
)
0
)
0
)
)
(
x3
(
λ x9 .
x5
)
0
0
)
)
=
setsum
(
setsum
(
x3
(
λ x9 .
x5
)
x5
(
setsum
(
x4
(
λ x9 .
λ x10 :
ι → ι
.
0
)
)
(
x6
(
λ x9 .
0
)
)
)
)
(
x3
(
λ x9 .
0
)
(
setsum
(
x0
(
λ x9 :
ι →
ι → ι
.
0
)
0
(
λ x9 .
0
)
)
0
)
(
setsum
(
x1
(
λ x9 .
λ x10 :
(
ι →
ι → ι
)
→
ι → ι
.
λ x11 .
0
)
(
λ x9 :
ι → ι
.
0
)
(
λ x9 :
(
ι → ι
)
→ ι
.
0
)
0
)
(
x7
(
λ x9 .
0
)
0
(
λ x9 .
0
)
0
)
)
)
)
(
x4
(
λ x9 .
λ x10 :
ι → ι
.
setsum
(
x6
(
λ x11 .
setsum
0
0
)
)
0
)
)
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
ι →
ι →
ι →
ι → ι
.
x0
(
λ x9 :
ι →
ι → ι
.
x5
)
(
x1
(
λ x9 .
λ x10 :
(
ι →
ι → ι
)
→
ι → ι
.
λ x11 .
Inj1
(
x3
(
λ x12 .
0
)
0
(
x1
(
λ x12 .
λ x13 :
(
ι →
ι → ι
)
→
ι → ι
.
λ x14 .
0
)
(
λ x12 :
ι → ι
.
0
)
(
λ x12 :
(
ι → ι
)
→ ι
.
0
)
0
)
)
)
(
λ x9 :
ι → ι
.
Inj0
(
x2
(
λ x10 .
x10
)
(
x1
(
λ x10 .
λ x11 :
(
ι →
ι → ι
)
→
ι → ι
.
λ x12 .
0
)
(
λ x10 :
ι → ι
.
0
)
(
λ x10 :
(
ι → ι
)
→ ι
.
0
)
0
)
)
)
(
λ x9 :
(
ι → ι
)
→ ι
.
0
)
(
x3
(
λ x9 .
0
)
0
(
x1
(
λ x9 .
λ x10 :
(
ι →
ι → ι
)
→
ι → ι
.
λ x11 .
Inj0
0
)
(
λ x9 :
ι → ι
.
x0
(
λ x10 :
ι →
ι → ι
.
0
)
0
(
λ x10 .
0
)
)
(
λ x9 :
(
ι → ι
)
→ ι
.
Inj0
0
)
0
)
)
)
(
λ x9 .
x1
(
λ x10 .
λ x11 :
(
ι →
ι → ι
)
→
ι → ι
.
λ x12 .
x12
)
(
λ x10 :
ι → ι
.
x1
(
λ x11 .
λ x12 :
(
ι →
ι → ι
)
→
ι → ι
.
λ x13 .
Inj1
(
x3
(
λ x14 .
0
)
0
0
)
)
(
λ x11 :
ι → ι
.
x9
)
(
λ x11 :
(
ι → ι
)
→ ι
.
x0
(
λ x12 :
ι →
ι → ι
.
x1
(
λ x13 .
λ x14 :
(
ι →
ι → ι
)
→
ι → ι
.
λ x15 .
0
)
(
λ x13 :
ι → ι
.
0
)
(
λ x13 :
(
ι → ι
)
→ ι
.
0
)
0
)
0
(
λ x12 .
0
)
)
(
setsum
(
x2
(
λ x11 .
0
)
0
)
(
x7
0
0
0
0
)
)
)
(
λ x10 :
(
ι → ι
)
→ ι
.
0
)
(
Inj0
(
x2
(
λ x10 .
Inj1
0
)
0
)
)
)
=
x1
(
λ x9 .
λ x10 :
(
ι →
ι → ι
)
→
ι → ι
.
λ x11 .
x9
)
(
λ x9 :
ι → ι
.
x3
(
λ x10 .
x9
(
setsum
0
0
)
)
(
setsum
0
(
x1
(
λ x10 .
λ x11 :
(
ι →
ι → ι
)
→
ι → ι
.
λ x12 .
x3
(
λ x13 .
0
)
0
0
)
(
λ x10 :
ι → ι
.
x1
(
λ x11 .
λ x12 :
(
ι →
ι → ι
)
→
ι → ι
.
λ x13 .
0
)
(
λ x11 :
ι → ι
.
0
)
(
λ x11 :
(
ι → ι
)
→ ι
.
0
)
0
)
(
λ x10 :
(
ι → ι
)
→ ι
.
x3
(
λ x11 .
0
)
0
0
)
0
)
)
0
)
(
λ x9 :
(
ι → ι
)
→ ι
.
Inj1
(
x0
(
λ x10 :
ι →
ι → ι
.
x3
(
λ x11 .
x2
(
λ x12 .
0
)
0
)
(
x2
(
λ x11 .
0
)
0
)
(
x3
(
λ x11 .
0
)
0
0
)
)
0
(
λ x10 .
x1
(
λ x11 .
λ x12 :
(
ι →
ι → ι
)
→
ι → ι
.
λ x13 .
Inj0
0
)
(
λ x11 :
ι → ι
.
Inj0
0
)
(
λ x11 :
(
ι → ι
)
→ ι
.
x3
(
λ x12 .
0
)
0
0
)
(
Inj1
0
)
)
)
)
(
Inj0
x5
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
(
(
ι →
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x7 :
ι → ι
.
x0
(
λ x9 :
ι →
ι → ι
.
0
)
(
x7
(
x3
(
λ x9 .
x2
(
λ x10 .
x3
(
λ x11 .
0
)
0
0
)
(
Inj0
0
)
)
(
setsum
0
x5
)
0
)
)
(
λ x9 .
x9
)
=
x7
(
setsum
0
0
)
)
⟶
False
(proof)
Theorem
1823d..
:
∀ x0 :
(
(
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
∀ x1 :
(
ι →
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→
ι → ι
.
∀ x2 :
(
(
ι →
ι → ι
)
→
ι → ι
)
→
ι →
(
ι →
ι → ι
)
→ ι
.
∀ x3 :
(
ι → ι
)
→
ι →
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
.
(
∀ x4 x5 .
∀ x6 :
ι → ι
.
∀ x7 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
x3
(
λ x9 .
Inj0
(
setsum
0
(
Inj1
x9
)
)
)
(
setsum
0
x4
)
(
λ x9 :
(
ι → ι
)
→ ι
.
x5
)
=
setsum
(
x1
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→
ι → ι
.
x0
(
λ x12 x13 :
ι → ι
.
Inj1
(
setsum
0
0
)
)
(
Inj1
0
)
(
x0
(
λ x12 x13 :
ι → ι
.
x2
(
λ x14 :
ι →
ι → ι
.
λ x15 .
0
)
0
(
λ x14 x15 .
0
)
)
(
Inj0
0
)
(
x7
0
(
λ x12 :
ι → ι
.
λ x13 .
0
)
(
λ x12 .
0
)
)
)
)
(
λ x9 x10 .
0
)
(
setsum
x5
(
x7
x4
(
λ x9 :
ι → ι
.
λ x10 .
x2
(
λ x11 :
ι →
ι → ι
.
λ x12 .
0
)
0
(
λ x11 x12 .
0
)
)
(
λ x9 .
x6
0
)
)
)
)
0
)
⟶
(
∀ x4 .
∀ x5 :
(
(
ι →
ι → ι
)
→ ι
)
→ ι
.
∀ x6 .
∀ x7 :
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
x3
(
λ x9 .
x1
(
λ x10 x11 .
λ x12 :
(
ι → ι
)
→
ι → ι
.
x12
(
λ x13 .
x2
(
λ x14 :
ι →
ι → ι
.
λ x15 .
x3
(
λ x16 .
0
)
0
(
λ x16 :
(
ι → ι
)
→ ι
.
0
)
)
(
setsum
0
0
)
(
λ x14 x15 .
x12
(
λ x16 .
0
)
0
)
)
(
x0
(
λ x13 x14 :
ι → ι
.
x13
0
)
(
setsum
0
0
)
x11
)
)
(
λ x10 .
Inj0
)
(
x1
(
λ x10 x11 .
λ x12 :
(
ι → ι
)
→
ι → ι
.
x3
(
λ x13 .
0
)
(
x2
(
λ x13 :
ι →
ι → ι
.
λ x14 .
0
)
0
(
λ x13 x14 .
0
)
)
(
λ x13 :
(
ι → ι
)
→ ι
.
x2
(
λ x14 :
ι →
ι → ι
.
λ x15 .
0
)
0
(
λ x14 x15 .
0
)
)
)
(
λ x10 x11 .
x0
(
λ x12 x13 :
ι → ι
.
x2
(
λ x14 :
ι →
ι → ι
.
λ x15 .
0
)
0
(
λ x14 x15 .
0
)
)
(
x0
(
λ x12 x13 :
ι → ι
.
0
)
0
0
)
(
setsum
0
0
)
)
(
Inj0
x9
)
)
)
x6
(
λ x9 :
(
ι → ι
)
→ ι
.
Inj1
0
)
=
Inj0
(
x7
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
x3
(
λ x11 .
Inj1
(
Inj0
0
)
)
0
(
λ x11 :
(
ι → ι
)
→ ι
.
Inj1
(
x10
0
)
)
)
)
)
⟶
(
∀ x4 :
ι →
ι → ι
.
∀ x5 x6 .
∀ x7 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
x2
(
λ x9 :
ι →
ι → ι
.
λ x10 .
setsum
0
(
x7
(
x0
(
λ x11 x12 :
ι → ι
.
x0
(
λ x13 x14 :
ι → ι
.
0
)
0
0
)
(
x0
(
λ x11 x12 :
ι → ι
.
0
)
0
0
)
)
(
λ x11 :
ι → ι
.
λ x12 .
Inj0
(
Inj1
0
)
)
)
)
(
x7
(
λ x9 .
x5
)
(
λ x9 :
ι → ι
.
λ x10 .
setsum
(
x3
(
λ x11 .
x3
(
λ x12 .
0
)
0
(
λ x12 :
(
ι → ι
)
→ ι
.
0
)
)
0
(
λ x11 :
(
ι → ι
)
→ ι
.
0
)
)
x6
)
)
(
λ x9 x10 .
setsum
0
0
)
=
x7
(
λ x9 .
x6
)
(
λ x9 :
ι → ι
.
λ x10 .
setsum
(
x2
(
λ x11 :
ι →
ι → ι
.
λ x12 .
x3
(
λ x13 .
setsum
0
0
)
(
setsum
0
0
)
(
λ x13 :
(
ι → ι
)
→ ι
.
0
)
)
(
Inj0
0
)
(
λ x11 x12 .
x9
(
setsum
0
0
)
)
)
(
x3
(
λ x11 .
x3
(
λ x12 .
Inj1
0
)
(
x1
(
λ x12 x13 .
λ x14 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x12 x13 .
0
)
0
)
(
λ x12 :
(
ι → ι
)
→ ι
.
0
)
)
(
Inj0
x6
)
(
λ x11 :
(
ι → ι
)
→ ι
.
x2
(
λ x12 :
ι →
ι → ι
.
λ x13 .
setsum
0
0
)
(
x1
(
λ x12 x13 .
λ x14 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x12 x13 .
0
)
0
)
(
λ x12 x13 .
0
)
)
)
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x5 .
∀ x6 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x7 .
x2
(
λ x9 :
ι →
ι → ι
.
λ x10 .
x7
)
x5
(
λ x9 x10 .
x0
(
λ x11 x12 :
ι → ι
.
x11
(
x2
(
λ x13 :
ι →
ι → ι
.
λ x14 .
setsum
0
0
)
0
(
λ x13 x14 .
setsum
0
0
)
)
)
0
(
x2
(
λ x11 :
ι →
ι → ι
.
λ x12 .
setsum
(
x3
(
λ x13 .
0
)
0
(
λ x13 :
(
ι → ι
)
→ ι
.
0
)
)
(
x2
(
λ x13 :
ι →
ι → ι
.
λ x14 .
0
)
0
(
λ x13 x14 .
0
)
)
)
(
setsum
(
x2
(
λ x11 :
ι →
ι → ι
.
λ x12 .
0
)
0
(
λ x11 x12 .
0
)
)
(
x6
(
λ x11 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x11 :
ι → ι
.
0
)
(
λ x11 .
0
)
0
)
)
(
λ x11 x12 .
x0
(
λ x13 x14 :
ι → ι
.
x13
0
)
(
x2
(
λ x13 :
ι →
ι → ι
.
λ x14 .
0
)
0
(
λ x13 x14 .
0
)
)
(
x0
(
λ x13 x14 :
ι → ι
.
0
)
0
0
)
)
)
)
=
x0
(
λ x9 x10 :
ι → ι
.
x7
)
(
x2
(
λ x9 :
ι →
ι → ι
.
λ x10 .
setsum
(
setsum
(
Inj1
0
)
(
x0
(
λ x11 x12 :
ι → ι
.
0
)
0
0
)
)
0
)
0
(
λ x9 x10 .
x3
(
λ x11 .
0
)
x10
(
λ x11 :
(
ι → ι
)
→ ι
.
x10
)
)
)
x5
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 x6 .
∀ x7 :
ι → ι
.
x1
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x9 x10 .
setsum
(
setsum
(
Inj0
(
x0
(
λ x11 x12 :
ι → ι
.
0
)
0
0
)
)
(
setsum
0
(
x2
(
λ x11 :
ι →
ι → ι
.
λ x12 .
0
)
0
(
λ x11 x12 .
0
)
)
)
)
(
setsum
(
x7
(
x2
(
λ x11 :
ι →
ι → ι
.
λ x12 .
0
)
0
(
λ x11 x12 .
0
)
)
)
x9
)
)
(
x3
(
λ x9 .
x3
(
λ x10 .
0
)
x5
(
λ x10 :
(
ι → ι
)
→ ι
.
x9
)
)
(
Inj1
(
Inj1
(
setsum
0
0
)
)
)
(
λ x9 :
(
ι → ι
)
→ ι
.
x2
(
λ x10 :
ι →
ι → ι
.
λ x11 .
x10
(
x0
(
λ x12 x13 :
ι → ι
.
0
)
0
0
)
(
Inj0
0
)
)
0
(
λ x10 x11 .
x1
(
λ x12 x13 .
λ x14 :
(
ι → ι
)
→
ι → ι
.
setsum
0
0
)
(
λ x12 x13 .
Inj0
0
)
(
setsum
0
0
)
)
)
)
=
Inj1
(
Inj1
x6
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x5 x6 x7 .
x1
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x9 x10 .
0
)
0
=
x7
)
⟶
(
∀ x4 x5 .
∀ x6 :
ι →
ι → ι
.
∀ x7 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
x0
(
λ x9 x10 :
ι → ι
.
x7
(
Inj0
0
)
(
x9
(
x2
(
λ x11 :
ι →
ι → ι
.
λ x12 .
Inj0
0
)
(
x1
(
λ x11 x12 .
λ x13 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x11 x12 .
0
)
0
)
(
λ x11 x12 .
x1
(
λ x13 x14 .
λ x15 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x13 x14 .
0
)
0
)
)
)
(
λ x11 .
x0
(
λ x12 x13 :
ι → ι
.
0
)
(
x2
(
λ x12 :
ι →
ι → ι
.
λ x13 .
0
)
0
(
λ x12 x13 .
0
)
)
(
x2
(
λ x12 :
ι →
ι → ι
.
λ x13 .
x12
0
0
)
(
Inj0
0
)
(
λ x12 x13 .
x1
(
λ x14 x15 .
λ x16 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x14 x15 .
0
)
0
)
)
)
(
x0
(
λ x11 x12 :
ι → ι
.
Inj0
(
setsum
0
0
)
)
(
x10
(
x0
(
λ x11 x12 :
ι → ι
.
0
)
0
0
)
)
(
x0
(
λ x11 x12 :
ι → ι
.
x11
0
)
(
x9
0
)
(
x0
(
λ x11 x12 :
ι → ι
.
0
)
0
0
)
)
)
)
0
0
=
setsum
(
setsum
(
setsum
x5
(
x2
(
λ x9 :
ι →
ι → ι
.
λ x10 .
x3
(
λ x11 .
0
)
0
(
λ x11 :
(
ι → ι
)
→ ι
.
0
)
)
(
x1
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x9 x10 .
0
)
0
)
(
λ x9 x10 .
x9
)
)
)
0
)
(
x7
(
setsum
(
x7
(
setsum
0
0
)
(
x7
0
0
(
λ x9 .
0
)
0
)
(
λ x9 .
x1
(
λ x10 x11 .
λ x12 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x10 x11 .
0
)
0
)
0
)
(
x0
(
λ x9 x10 :
ι → ι
.
x6
0
0
)
(
x3
(
λ x9 .
0
)
0
(
λ x9 :
(
ι → ι
)
→ ι
.
0
)
)
(
setsum
0
0
)
)
)
(
x6
0
(
setsum
(
x0
(
λ x9 x10 :
ι → ι
.
0
)
0
0
)
(
setsum
0
0
)
)
)
(
λ x9 .
x2
(
λ x10 :
ι →
ι → ι
.
λ x11 .
x0
(
λ x12 x13 :
ι → ι
.
0
)
0
(
x2
(
λ x12 :
ι →
ι → ι
.
λ x13 .
0
)
0
(
λ x12 x13 .
0
)
)
)
0
(
λ x10 x11 .
x7
x9
(
x3
(
λ x12 .
0
)
0
(
λ x12 :
(
ι → ι
)
→ ι
.
0
)
)
(
λ x12 .
0
)
0
)
)
(
Inj0
(
x7
(
x3
(
λ x9 .
0
)
0
(
λ x9 :
(
ι → ι
)
→ ι
.
0
)
)
(
x0
(
λ x9 x10 :
ι → ι
.
0
)
0
0
)
(
λ x9 .
x7
0
0
(
λ x10 .
0
)
0
)
(
x1
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x9 x10 .
0
)
0
)
)
)
)
)
⟶
(
∀ x4 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x5 .
∀ x6 :
ι → ι
.
∀ x7 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
x0
(
λ x9 x10 :
ι → ι
.
0
)
0
0
=
x7
(
x0
(
λ x9 x10 :
ι → ι
.
x9
(
x0
(
λ x11 x12 :
ι → ι
.
x12
0
)
(
Inj0
0
)
(
x6
0
)
)
)
(
Inj1
0
)
(
x0
(
λ x9 x10 :
ι → ι
.
x0
(
λ x11 x12 :
ι → ι
.
x3
(
λ x13 .
0
)
0
(
λ x13 :
(
ι → ι
)
→ ι
.
0
)
)
0
(
x10
0
)
)
x5
(
x4
(
x1
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x9 x10 .
0
)
0
)
(
λ x9 :
ι → ι
.
λ x10 .
setsum
0
0
)
(
λ x9 .
0
)
(
x1
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x9 x10 .
0
)
0
)
)
)
)
(
λ x9 :
ι → ι
.
λ x10 .
x3
(
λ x11 .
x11
)
(
Inj0
(
setsum
(
setsum
0
0
)
(
Inj1
0
)
)
)
(
λ x11 :
(
ι → ι
)
→ ι
.
0
)
)
)
⟶
False
(proof)
Theorem
ebf15..
:
∀ x0 :
(
ι →
ι → ι
)
→
ι →
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
∀ x1 :
(
(
ι →
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→
ι →
(
ι → ι
)
→ ι
)
→ ι
.
∀ x2 :
(
ι →
ι →
ι → ι
)
→
(
(
ι →
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x3 :
(
ι → ι
)
→
(
(
ι → ι
)
→
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
(
∀ x4 x5 .
∀ x6 :
ι → ι
.
∀ x7 .
x3
(
λ x9 .
x6
(
Inj1
x7
)
)
(
λ x9 :
ι → ι
.
λ x10 :
ι →
ι → ι
.
λ x11 :
ι → ι
.
λ x12 .
0
)
=
Inj1
(
setsum
(
x3
(
λ x9 .
x9
)
(
λ x9 :
ι → ι
.
λ x10 :
ι →
ι → ι
.
λ x11 :
ι → ι
.
λ x12 .
Inj0
(
x10
0
0
)
)
)
(
Inj0
(
x1
(
λ x9 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x9 :
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
0
)
)
)
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x5 .
∀ x6 :
ι → ι
.
∀ x7 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
x3
(
λ x9 .
x9
)
(
λ x9 :
ι → ι
.
λ x10 :
ι →
ι → ι
.
λ x11 :
ι → ι
.
λ x12 .
0
)
=
Inj1
0
)
⟶
(
∀ x4 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x5 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x6 x7 .
x2
(
λ x9 x10 x11 .
setsum
x7
0
)
(
λ x9 :
ι →
ι → ι
.
λ x10 .
x0
(
λ x11 x12 .
x12
)
0
(
λ x11 .
λ x12 :
ι → ι
.
Inj0
x11
)
)
=
x0
(
λ x9 x10 .
Inj1
0
)
(
x5
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 .
0
)
(
λ x9 :
ι → ι
.
λ x10 .
x10
)
)
(
λ x9 .
λ x10 :
ι → ι
.
Inj1
(
x1
(
λ x11 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
x1
(
λ x12 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
Inj0
0
)
(
λ x12 :
ι → ι
.
λ x13 .
λ x14 :
ι → ι
.
0
)
)
(
λ x11 :
ι → ι
.
λ x12 .
λ x13 :
ι → ι
.
0
)
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 :
ι →
(
ι →
ι → ι
)
→ ι
.
∀ x6 :
(
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x7 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
.
x2
(
λ x9 x10 x11 .
x11
)
(
λ x9 :
ι →
ι → ι
.
λ x10 .
0
)
=
x6
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 .
x6
(
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 .
x3
(
λ x13 .
0
)
(
λ x13 :
ι → ι
.
λ x14 :
ι →
ι → ι
.
λ x15 :
ι → ι
.
λ x16 .
x3
(
λ x17 .
0
)
(
λ x17 :
ι → ι
.
λ x18 :
ι →
ι → ι
.
λ x19 :
ι → ι
.
λ x20 .
0
)
)
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 .
∀ x6 :
(
ι → ι
)
→
ι →
(
ι → ι
)
→ ι
.
∀ x7 .
x1
(
λ x9 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
Inj1
(
x6
(
λ x10 .
x7
)
(
setsum
0
x5
)
(
λ x10 .
setsum
(
x2
(
λ x11 x12 x13 .
0
)
(
λ x11 :
ι →
ι → ι
.
λ x12 .
0
)
)
(
setsum
0
0
)
)
)
)
(
λ x9 :
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
setsum
(
Inj1
0
)
(
x3
(
λ x12 .
0
)
(
λ x12 :
ι → ι
.
λ x13 :
ι →
ι → ι
.
λ x14 :
ι → ι
.
λ x15 .
setsum
(
x13
0
0
)
(
x2
(
λ x16 x17 x18 .
0
)
(
λ x16 :
ι →
ι → ι
.
λ x17 .
0
)
)
)
)
)
=
setsum
(
Inj1
x7
)
(
Inj1
(
setsum
(
x4
(
x6
(
λ x9 .
0
)
0
(
λ x9 .
0
)
)
)
(
x3
(
λ x9 .
x0
(
λ x10 x11 .
0
)
0
(
λ x10 .
λ x11 :
ι → ι
.
0
)
)
(
λ x9 :
ι → ι
.
λ x10 :
ι →
ι → ι
.
λ x11 :
ι → ι
.
λ x12 .
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 :
(
ι →
(
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→
ι →
ι → ι
.
∀ x5 :
(
ι → ι
)
→ ι
.
∀ x6 x7 :
ι → ι
.
x1
(
λ x9 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x9 :
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
setsum
(
x1
(
λ x12 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x12 :
ι → ι
.
λ x13 .
λ x14 :
ι → ι
.
0
)
)
(
x7
(
Inj0
(
x11
0
)
)
)
)
=
setsum
(
x1
(
λ x9 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
Inj1
0
)
(
λ x9 :
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
x3
(
λ x12 .
0
)
(
λ x12 :
ι → ι
.
λ x13 :
ι →
ι → ι
.
λ x14 :
ι → ι
.
λ x15 .
x12
(
x14
0
)
)
)
)
(
x7
0
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→ ι
.
∀ x5 x6 x7 .
x0
(
λ x9 x10 .
setsum
(
x0
(
λ x11 x12 .
0
)
(
Inj0
(
x2
(
λ x11 x12 x13 .
0
)
(
λ x11 :
ι →
ι → ι
.
λ x12 .
0
)
)
)
(
λ x11 .
λ x12 :
ι → ι
.
Inj1
(
x2
(
λ x13 x14 x15 .
0
)
(
λ x13 :
ι →
ι → ι
.
λ x14 .
0
)
)
)
)
0
)
x5
(
λ x9 .
λ x10 :
ι → ι
.
x7
)
=
Inj0
x5
)
⟶
(
∀ x4 :
ι →
ι →
(
ι → ι
)
→ ι
.
∀ x5 :
(
ι →
ι →
ι → ι
)
→
ι → ι
.
∀ x6 .
∀ x7 :
(
(
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
ι →
ι →
ι → ι
.
x0
(
λ x9 x10 .
x9
)
(
Inj1
(
Inj0
(
x2
(
λ x9 x10 x11 .
setsum
0
0
)
(
λ x9 :
ι →
ι → ι
.
λ x10 .
0
)
)
)
)
(
λ x9 .
λ x10 :
ι → ι
.
0
)
=
setsum
x6
(
x7
(
λ x9 x10 :
ι → ι
.
x0
(
λ x11 x12 .
x2
(
λ x13 x14 x15 .
x14
)
(
λ x13 :
ι →
ι → ι
.
λ x14 .
0
)
)
x6
(
λ x11 .
λ x12 :
ι → ι
.
Inj1
(
x9
0
)
)
)
(
Inj0
0
)
0
(
x7
(
λ x9 x10 :
ι → ι
.
x0
(
λ x11 x12 .
x1
(
λ x13 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x13 :
ι → ι
.
λ x14 .
λ x15 :
ι → ι
.
0
)
)
(
setsum
0
0
)
(
λ x11 .
λ x12 :
ι → ι
.
x9
0
)
)
x6
(
x3
(
λ x9 .
x1
(
λ x10 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x10 :
ι → ι
.
λ x11 .
λ x12 :
ι → ι
.
0
)
)
(
λ x9 :
ι → ι
.
λ x10 :
ι →
ι → ι
.
λ x11 :
ι → ι
.
λ x12 .
x11
0
)
)
(
setsum
(
x5
(
λ x9 x10 x11 .
0
)
0
)
(
x3
(
λ x9 .
0
)
(
λ x9 :
ι → ι
.
λ x10 :
ι →
ι → ι
.
λ x11 :
ι → ι
.
λ x12 .
0
)
)
)
)
)
)
⟶
False
(proof)
Theorem
269d3..
:
∀ x0 :
(
ι → ι
)
→
ι → ι
.
∀ x1 :
(
ι →
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι → ι
.
∀ x2 :
(
ι →
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι →
ι → ι
)
→
ι → ι
.
∀ x3 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι → ι
.
(
∀ x4 :
ι → ι
.
∀ x5 :
ι →
ι → ι
.
∀ x6 :
ι →
(
ι → ι
)
→
ι → ι
.
∀ x7 .
x3
(
λ x9 :
(
ι → ι
)
→ ι
.
Inj0
0
)
(
x6
(
setsum
0
0
)
(
λ x9 .
0
)
(
x4
0
)
)
=
x6
(
Inj0
(
Inj0
(
Inj1
(
Inj1
0
)
)
)
)
(
setsum
(
x2
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x11 :
ι → ι
.
λ x12 x13 .
x3
(
λ x14 :
(
ι → ι
)
→ ι
.
x2
(
λ x15 .
λ x16 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x17 :
ι → ι
.
λ x18 x19 .
0
)
0
)
(
x2
(
λ x14 .
λ x15 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x16 :
ι → ι
.
λ x17 x18 .
0
)
0
)
)
(
setsum
0
0
)
)
)
x7
)
⟶
(
∀ x4 :
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x5 :
ι →
(
ι → ι
)
→
ι → ι
.
∀ x6 x7 .
x3
(
λ x9 :
(
ι → ι
)
→ ι
.
Inj0
0
)
(
x3
(
λ x9 :
(
ι → ι
)
→ ι
.
0
)
(
x1
(
λ x9 .
λ x10 :
(
ι → ι
)
→ ι
.
x6
)
x7
)
)
=
x3
(
λ x9 :
(
ι → ι
)
→ ι
.
x5
0
(
λ x10 .
x1
(
λ x11 .
λ x12 :
(
ι → ι
)
→ ι
.
x3
(
λ x13 :
(
ι → ι
)
→ ι
.
0
)
(
x1
(
λ x13 .
λ x14 :
(
ι → ι
)
→ ι
.
0
)
0
)
)
(
Inj0
0
)
)
0
)
(
Inj0
(
x3
(
λ x9 :
(
ι → ι
)
→ ι
.
x0
(
λ x10 .
x9
(
λ x11 .
0
)
)
x7
)
x6
)
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
ι →
ι → ι
.
∀ x7 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
x2
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x11 :
ι → ι
.
λ x12 x13 .
Inj0
(
x2
(
λ x14 .
λ x15 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x16 :
ι → ι
.
λ x17 x18 .
0
)
0
)
)
(
setsum
(
setsum
(
Inj1
0
)
(
Inj1
(
x1
(
λ x9 .
λ x10 :
(
ι → ι
)
→ ι
.
0
)
0
)
)
)
0
)
=
Inj0
0
)
⟶
(
∀ x4 :
ι →
(
ι → ι
)
→
ι →
ι → ι
.
∀ x5 .
∀ x6 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
.
∀ x7 .
x2
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x11 :
ι → ι
.
λ x12 x13 .
x1
(
λ x14 .
λ x15 :
(
ι → ι
)
→ ι
.
x3
(
λ x16 :
(
ι → ι
)
→ ι
.
x3
(
λ x17 :
(
ι → ι
)
→ ι
.
0
)
(
Inj0
0
)
)
(
setsum
0
0
)
)
(
Inj0
x13
)
)
(
x0
(
λ x9 .
Inj1
(
setsum
(
x3
(
λ x10 :
(
ι → ι
)
→ ι
.
0
)
0
)
(
x3
(
λ x10 :
(
ι → ι
)
→ ι
.
0
)
0
)
)
)
(
setsum
(
setsum
(
x1
(
λ x9 .
λ x10 :
(
ι → ι
)
→ ι
.
0
)
0
)
0
)
(
Inj1
(
x3
(
λ x9 :
(
ι → ι
)
→ ι
.
0
)
0
)
)
)
)
=
setsum
(
setsum
(
x2
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x11 :
ι → ι
.
λ x12 x13 .
x13
)
(
x2
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x11 :
ι → ι
.
λ x12 x13 .
setsum
0
0
)
x7
)
)
0
)
(
setsum
(
x1
(
λ x9 .
λ x10 :
(
ι → ι
)
→ ι
.
0
)
x7
)
(
x3
(
λ x9 :
(
ι → ι
)
→ ι
.
x0
(
λ x10 .
x7
)
(
x1
(
λ x10 .
λ x11 :
(
ι → ι
)
→ ι
.
0
)
0
)
)
(
x4
(
x3
(
λ x9 :
(
ι → ι
)
→ ι
.
0
)
0
)
(
λ x9 .
setsum
0
0
)
(
x6
(
λ x9 .
λ x10 :
ι → ι
.
0
)
0
)
(
x6
(
λ x9 .
λ x10 :
ι → ι
.
0
)
0
)
)
)
)
)
⟶
(
∀ x4 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
.
∀ x5 .
∀ x6 :
ι →
ι →
ι → ι
.
∀ x7 :
ι → ι
.
x1
(
λ x9 .
λ x10 :
(
ι → ι
)
→ ι
.
x1
(
λ x11 .
λ x12 :
(
ι → ι
)
→ ι
.
setsum
x11
0
)
(
x10
(
λ x11 .
0
)
)
)
(
x4
(
λ x9 .
λ x10 :
ι → ι
.
setsum
(
Inj1
(
x3
(
λ x11 :
(
ι → ι
)
→ ι
.
0
)
0
)
)
(
x1
(
λ x11 .
λ x12 :
(
ι → ι
)
→ ι
.
x10
0
)
(
x1
(
λ x11 .
λ x12 :
(
ι → ι
)
→ ι
.
0
)
0
)
)
)
0
)
=
setsum
(
setsum
0
(
x4
(
λ x9 .
λ x10 :
ι → ι
.
x6
0
(
x6
0
0
0
)
(
x1
(
λ x11 .
λ x12 :
(
ι → ι
)
→ ι
.
0
)
0
)
)
(
x1
(
λ x9 .
λ x10 :
(
ι → ι
)
→ ι
.
Inj0
0
)
(
setsum
0
0
)
)
)
)
(
x7
(
setsum
(
x4
(
λ x9 .
λ x10 :
ι → ι
.
x1
(
λ x11 .
λ x12 :
(
ι → ι
)
→ ι
.
0
)
0
)
(
x7
0
)
)
(
setsum
(
setsum
0
0
)
(
x7
0
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
∀ x6 :
(
(
ι →
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x7 .
x1
(
λ x9 .
λ x10 :
(
ι → ι
)
→ ι
.
x3
(
λ x11 :
(
ι → ι
)
→ ι
.
x3
(
λ x12 :
(
ι → ι
)
→ ι
.
0
)
(
setsum
(
Inj0
0
)
(
x10
(
λ x12 .
0
)
)
)
)
0
)
(
x3
(
λ x9 :
(
ι → ι
)
→ ι
.
x0
(
λ x10 .
x10
)
(
x3
(
λ x10 :
(
ι → ι
)
→ ι
.
0
)
(
Inj0
0
)
)
)
(
Inj1
(
setsum
(
x1
(
λ x9 .
λ x10 :
(
ι → ι
)
→ ι
.
0
)
0
)
x7
)
)
)
=
Inj1
0
)
⟶
(
∀ x4 :
(
ι →
ι → ι
)
→ ι
.
∀ x5 x6 .
∀ x7 :
ι →
ι → ι
.
x0
(
λ x9 .
0
)
0
=
x4
(
λ x9 x10 .
x7
0
(
Inj0
0
)
)
)
⟶
(
∀ x4 x5 x6 x7 .
x0
(
λ x9 .
x0
(
λ x10 .
x1
(
λ x11 .
λ x12 :
(
ι → ι
)
→ ι
.
0
)
x9
)
x9
)
(
setsum
0
(
x1
(
λ x9 .
λ x10 :
(
ι → ι
)
→ ι
.
x0
(
λ x11 .
x1
(
λ x12 .
λ x13 :
(
ι → ι
)
→ ι
.
0
)
0
)
(
x2
(
λ x11 .
λ x12 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x13 :
ι → ι
.
λ x14 x15 .
0
)
0
)
)
(
x0
(
λ x9 .
0
)
0
)
)
)
=
setsum
(
x2
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x11 :
ι → ι
.
λ x12 x13 .
0
)
0
)
0
)
⟶
False
(proof)
Theorem
aa86e..
:
∀ x0 :
(
ι →
ι → ι
)
→
(
(
ι →
ι →
ι → ι
)
→
ι → ι
)
→
ι → ι
.
∀ x1 :
(
(
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
)
→
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
∀ x2 :
(
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι →
ι → ι
)
→
ι → ι
.
∀ x3 :
(
ι →
ι →
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
.
(
∀ x4 :
ι →
(
ι →
ι → ι
)
→
ι →
ι → ι
.
∀ x5 x6 x7 .
x3
(
λ x9 x10 x11 .
λ x12 :
ι → ι
.
0
)
x7
=
x7
)
⟶
(
∀ x4 x5 x6 x7 .
x3
(
λ x9 x10 x11 .
λ x12 :
ι → ι
.
x2
(
λ x13 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x14 x15 .
Inj0
(
Inj0
(
setsum
0
0
)
)
)
(
x12
(
x2
(
λ x13 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x14 x15 .
x2
(
λ x16 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x17 x18 .
0
)
0
)
0
)
)
)
(
x3
(
λ x9 x10 x11 .
λ x12 :
ι → ι
.
x0
(
λ x13 x14 .
x1
(
λ x15 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
λ x16 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x17 :
(
ι → ι
)
→
ι → ι
.
x14
)
(
λ x15 .
0
)
)
(
λ x13 :
ι →
ι →
ι → ι
.
λ x14 .
0
)
(
Inj0
(
Inj0
0
)
)
)
(
x2
(
λ x9 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 x11 .
x3
(
λ x12 x13 x14 .
λ x15 :
ι → ι
.
0
)
(
Inj1
0
)
)
(
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
)
=
Inj1
0
)
⟶
(
∀ x4 x5 .
∀ x6 :
ι →
ι → ι
.
∀ x7 .
x2
(
λ x9 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 x11 .
x0
(
λ x12 x13 .
x11
)
(
λ x12 :
ι →
ι →
ι → ι
.
λ x13 .
x2
(
λ x14 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x15 x16 .
Inj1
0
)
x11
)
(
x0
(
λ x12 x13 .
x2
(
λ x14 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x15 x16 .
x15
)
0
)
(
λ x12 :
ι →
ι →
ι → ι
.
λ x13 .
Inj1
(
x12
0
0
0
)
)
0
)
)
x7
=
setsum
0
(
setsum
(
setsum
x7
(
Inj1
x5
)
)
(
x0
(
λ x9 x10 .
0
)
(
λ x9 :
ι →
ι →
ι → ι
.
λ x10 .
x10
)
0
)
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x5 x6 :
ι → ι
.
∀ x7 .
x2
(
λ x9 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 x11 .
0
)
x7
=
x7
)
⟶
(
∀ x4 :
ι →
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x5 :
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x6 :
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
∀ x7 .
x1
(
λ x9 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x11 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x9 .
x2
(
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 x12 .
0
)
(
x0
(
λ x10 x11 .
x9
)
(
λ x10 :
ι →
ι →
ι → ι
.
λ x11 .
0
)
(
x3
(
λ x10 x11 x12 .
λ x13 :
ι → ι
.
0
)
x9
)
)
)
=
setsum
(
x2
(
λ x9 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 x11 .
setsum
(
Inj0
(
setsum
0
0
)
)
(
x9
(
λ x12 :
ι → ι
.
0
)
)
)
0
)
0
)
⟶
(
∀ x4 :
(
(
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x5 x6 .
∀ x7 :
(
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
x1
(
λ x9 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x11 :
(
ι → ι
)
→
ι → ι
.
setsum
(
Inj1
(
x9
(
λ x12 :
ι →
ι → ι
.
λ x13 :
ι → ι
.
x2
(
λ x14 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x15 x16 .
0
)
0
)
)
)
0
)
(
λ x9 .
x9
)
=
x4
(
λ x9 x10 :
ι → ι
.
x0
(
λ x11 .
x2
(
λ x12 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x13 x14 .
x14
)
)
(
λ x11 :
ι →
ι →
ι → ι
.
λ x12 .
x0
(
λ x13 x14 .
x2
(
λ x15 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x16 x17 .
Inj0
0
)
(
Inj1
0
)
)
(
λ x13 :
ι →
ι →
ι → ι
.
λ x14 .
x0
(
λ x15 x16 .
x15
)
(
λ x15 :
ι →
ι →
ι → ι
.
λ x16 .
setsum
0
0
)
(
x0
(
λ x15 x16 .
0
)
(
λ x15 :
ι →
ι →
ι → ι
.
λ x16 .
0
)
0
)
)
0
)
(
Inj0
0
)
)
(
λ x9 .
x3
(
λ x10 x11 x12 .
λ x13 :
ι → ι
.
0
)
x6
)
(
x7
(
λ x9 .
x6
)
(
λ x9 :
ι → ι
.
λ x10 .
Inj0
(
Inj1
0
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 .
∀ x7 :
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→
ι →
ι → ι
.
x0
(
λ x9 x10 .
x2
(
λ x11 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x12 x13 .
0
)
(
x1
(
λ x11 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
λ x12 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x13 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x11 .
x3
(
λ x12 x13 x14 .
λ x15 :
ι → ι
.
x14
)
(
setsum
0
0
)
)
)
)
(
λ x9 :
ι →
ι →
ι → ι
.
λ x10 .
Inj1
(
x3
(
λ x11 x12 x13 .
λ x14 :
ι → ι
.
setsum
(
Inj1
0
)
0
)
0
)
)
(
x2
(
λ x9 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 x11 .
x2
(
λ x12 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x13 x14 .
0
)
0
)
(
Inj1
(
Inj1
(
x7
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
0
)
(
λ x9 x10 .
0
)
0
0
)
)
)
)
=
x2
(
λ x9 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 x11 .
Inj1
(
setsum
0
0
)
)
(
setsum
(
x2
(
λ x9 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 x11 .
x7
(
λ x12 :
(
ι → ι
)
→ ι
.
λ x13 :
ι → ι
.
0
)
(
λ x12 x13 .
x13
)
(
x1
(
λ x12 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
λ x13 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x14 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x12 .
0
)
)
x10
)
0
)
0
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→ ι
.
∀ x5 x6 .
∀ x7 :
ι → ι
.
x0
(
λ x9 x10 .
0
)
(
λ x9 :
ι →
ι →
ι → ι
.
λ x10 .
Inj1
0
)
0
=
x5
)
⟶
False
(proof)
Theorem
813f2..
:
∀ x0 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
∀ x1 :
(
(
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x2 :
(
(
ι → ι
)
→
ι → ι
)
→
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x3 :
(
(
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→
ι →
ι → ι
)
→
ι → ι
.
(
∀ x4 .
∀ x5 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
.
∀ x6 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x7 :
ι →
ι →
(
ι → ι
)
→ ι
.
x3
(
λ x9 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
λ x12 x13 .
0
)
(
Inj1
(
x1
(
λ x9 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x10 :
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
x3
(
λ x11 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x12 .
λ x13 :
ι → ι
.
λ x14 x15 .
0
)
(
x10
(
λ x11 .
0
)
(
λ x11 .
0
)
0
)
)
(
λ x9 :
ι → ι
.
λ x10 .
Inj1
(
x2
(
λ x11 :
ι → ι
.
λ x12 .
0
)
0
(
λ x11 :
ι → ι
.
λ x12 .
0
)
)
)
)
)
=
setsum
(
Inj0
(
Inj0
(
x3
(
λ x9 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
λ x12 x13 .
setsum
0
0
)
(
x1
(
λ x9 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x10 :
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x9 :
ι → ι
.
λ x10 .
0
)
)
)
)
)
(
Inj1
(
x7
(
x7
(
Inj0
0
)
0
(
λ x9 .
x6
(
λ x10 :
(
ι → ι
)
→ ι
.
0
)
(
λ x10 .
0
)
0
)
)
0
(
λ x9 .
setsum
(
Inj0
0
)
(
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 .
∀ x6 :
ι → ι
.
∀ x7 .
x3
(
λ x9 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
λ x12 x13 .
x13
)
(
setsum
(
x0
(
λ x9 .
x2
(
λ x10 :
ι → ι
.
λ x11 .
0
)
(
Inj1
0
)
(
λ x10 :
ι → ι
.
λ x11 .
setsum
0
0
)
)
(
λ x9 x10 .
x9
)
)
(
x2
(
λ x9 :
ι → ι
.
λ x10 .
Inj1
(
x0
(
λ x11 .
0
)
(
λ x11 x12 .
0
)
)
)
(
setsum
(
x6
0
)
(
x0
(
λ x9 .
0
)
(
λ x9 x10 .
0
)
)
)
(
λ x9 :
ι → ι
.
λ x10 .
setsum
(
Inj0
0
)
0
)
)
)
=
x7
)
⟶
(
∀ x4 x5 x6 x7 .
x2
(
λ x9 :
ι → ι
.
λ x10 .
setsum
(
x2
(
λ x11 :
ι → ι
.
λ x12 .
setsum
0
0
)
(
Inj0
(
x9
0
)
)
(
λ x11 :
ι → ι
.
λ x12 .
Inj0
(
Inj0
0
)
)
)
x7
)
x7
(
λ x9 :
ι → ι
.
λ x10 .
x0
(
λ x11 .
setsum
(
x3
(
λ x12 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x13 .
λ x14 :
ι → ι
.
λ x15 x16 .
x2
(
λ x17 :
ι → ι
.
λ x18 .
0
)
0
(
λ x17 :
ι → ι
.
λ x18 .
0
)
)
(
Inj0
0
)
)
0
)
(
λ x11 x12 .
x9
(
x1
(
λ x13 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x14 :
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
x13
(
λ x15 :
(
ι → ι
)
→
ι → ι
.
λ x16 :
ι → ι
.
λ x17 .
0
)
)
(
λ x13 :
ι → ι
.
λ x14 .
Inj1
0
)
)
)
)
=
x0
(
λ x9 .
Inj1
0
)
(
λ x9 x10 .
setsum
0
x9
)
)
⟶
(
∀ x4 .
∀ x5 x6 :
ι → ι
.
∀ x7 :
(
(
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
x2
(
λ x9 :
ι → ι
.
λ x10 .
x0
(
λ x11 .
x7
(
λ x12 :
ι → ι
.
λ x13 x14 .
setsum
x14
(
x3
(
λ x15 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x16 .
λ x17 :
ι → ι
.
λ x18 x19 .
0
)
0
)
)
)
(
λ x11 x12 .
0
)
)
0
(
λ x9 :
ι → ι
.
λ x10 .
setsum
(
x0
(
λ x11 .
x0
(
λ x12 .
x12
)
(
λ x12 x13 .
setsum
0
0
)
)
(
λ x11 x12 .
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
(
setsum
0
x10
)
)
=
Inj0
(
x1
(
λ x9 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x10 :
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
Inj1
(
x6
(
setsum
0
0
)
)
)
(
λ x9 :
ι → ι
.
λ x10 .
x9
0
)
)
)
⟶
(
∀ x4 x5 x6 x7 .
x1
(
λ x9 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x10 :
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
x0
(
λ x11 .
0
)
(
λ x11 x12 .
0
)
)
(
λ x9 :
ι → ι
.
λ x10 .
x7
)
=
setsum
0
(
x3
(
λ x9 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x10 .
λ x11 :
ι → ι
.
λ x12 x13 .
x11
(
x2
(
λ x14 :
ι → ι
.
λ x15 .
0
)
(
Inj1
0
)
(
λ x14 :
ι → ι
.
λ x15 .
0
)
)
)
x7
)
)
⟶
(
∀ x4 :
(
ι →
ι →
ι → ι
)
→ ι
.
∀ x5 :
(
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
∀ x6 :
(
ι →
ι →
ι → ι
)
→
ι → ι
.
∀ x7 :
(
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
x1
(
λ x9 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x10 :
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x9 :
ι → ι
.
λ x10 .
0
)
=
setsum
0
(
setsum
(
x6
(
λ x9 x10 x11 .
x11
)
(
x1
(
λ x9 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x10 :
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
x7
(
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 x13 .
0
)
(
λ x11 :
ι → ι
.
λ x12 .
0
)
)
(
λ x9 :
ι → ι
.
λ x10 .
0
)
)
)
(
x0
(
λ x9 .
x9
)
(
λ x9 x10 .
setsum
(
x2
(
λ x11 :
ι → ι
.
λ x12 .
0
)
0
(
λ x11 :
ι → ι
.
λ x12 .
0
)
)
(
x7
(
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 x13 .
0
)
(
λ x11 :
ι → ι
.
λ x12 .
0
)
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→ ι
.
∀ x7 .
x0
(
λ x9 .
x5
0
)
(
λ x9 x10 .
0
)
=
setsum
0
0
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 .
∀ x6 :
ι → ι
.
∀ x7 :
(
ι →
ι →
ι → ι
)
→ ι
.
x0
(
λ x9 .
x2
(
λ x10 :
ι → ι
.
λ x11 .
setsum
0
x9
)
(
x0
(
λ x10 .
setsum
(
x7
(
λ x11 x12 x13 .
0
)
)
(
setsum
0
0
)
)
(
λ x10 x11 .
x10
)
)
(
λ x10 :
ι → ι
.
λ x11 .
x7
(
λ x12 x13 x14 .
x2
(
λ x15 :
ι → ι
.
λ x16 .
x14
)
(
Inj1
0
)
(
λ x15 :
ι → ι
.
λ x16 .
x16
)
)
)
)
(
λ x9 x10 .
x7
(
λ x11 x12 x13 .
x0
(
λ x14 .
0
)
(
λ x14 x15 .
Inj0
(
x0
(
λ x16 .
0
)
(
λ x16 x17 .
0
)
)
)
)
)
=
Inj1
(
x0
(
λ x9 .
0
)
(
λ x9 x10 .
0
)
)
)
⟶
False
(proof)
Theorem
f3264..
:
∀ x0 :
(
ι → ι
)
→
(
ι → ι
)
→
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
∀ x1 :
(
ι → ι
)
→
ι →
(
(
ι →
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
∀ x2 :
(
(
(
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
.
∀ x3 :
(
ι →
ι →
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
)
→
ι → ι
.
(
∀ x4 :
(
ι → ι
)
→ ι
.
∀ x5 :
ι → ι
.
∀ x6 .
∀ x7 :
ι → ι
.
x3
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 :
ι → ι
.
x0
(
λ x13 .
setsum
(
setsum
0
x13
)
0
)
(
λ x13 .
0
)
(
λ x13 :
(
ι → ι
)
→
ι → ι
.
λ x14 :
ι → ι
.
λ x15 .
0
)
(
x11
(
λ x13 .
x12
(
x12
0
)
)
)
(
Inj1
(
x3
(
λ x13 x14 .
λ x15 :
(
ι → ι
)
→ ι
.
λ x16 :
ι → ι
.
0
)
(
x3
(
λ x13 x14 .
λ x15 :
(
ι → ι
)
→ ι
.
λ x16 :
ι → ι
.
0
)
0
)
)
)
)
0
=
x0
(
λ x9 .
setsum
x9
(
x0
(
λ x10 .
x3
(
λ x11 x12 .
λ x13 :
(
ι → ι
)
→ ι
.
λ x14 :
ι → ι
.
x2
(
λ x15 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x16 :
(
ι →
ι → ι
)
→ ι
.
λ x17 :
(
ι → ι
)
→
ι → ι
.
0
)
0
(
λ x15 x16 .
0
)
)
x9
)
(
λ x10 .
x10
)
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 :
ι → ι
.
λ x12 .
Inj0
(
setsum
0
0
)
)
x6
x9
)
)
(
λ x9 .
setsum
(
x0
(
λ x10 .
0
)
(
λ x10 .
x10
)
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 :
ι → ι
.
λ x12 .
x9
)
(
Inj0
0
)
(
setsum
(
x3
(
λ x10 x11 .
λ x12 :
(
ι → ι
)
→ ι
.
λ x13 :
ι → ι
.
0
)
0
)
(
x3
(
λ x10 x11 .
λ x12 :
(
ι → ι
)
→ ι
.
λ x13 :
ι → ι
.
0
)
0
)
)
)
x9
)
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 :
ι → ι
.
λ x11 .
setsum
(
x2
(
λ x12 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x13 :
(
ι →
ι → ι
)
→ ι
.
λ x14 :
(
ι → ι
)
→
ι → ι
.
x14
(
λ x15 .
Inj1
0
)
0
)
(
Inj0
0
)
(
λ x12 x13 .
Inj0
(
Inj1
0
)
)
)
(
x10
(
x10
0
)
)
)
(
x0
(
λ x9 .
x9
)
(
λ x9 .
x2
(
λ x10 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x11 :
(
ι →
ι → ι
)
→ ι
.
λ x12 :
(
ι → ι
)
→
ι → ι
.
x12
(
λ x13 .
0
)
0
)
(
setsum
(
x1
(
λ x10 .
0
)
0
(
λ x10 :
ι →
ι → ι
.
0
)
(
λ x10 .
0
)
)
(
x0
(
λ x10 .
0
)
(
λ x10 .
0
)
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 :
ι → ι
.
λ x12 .
0
)
0
0
)
)
(
λ x10 x11 .
x9
)
)
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 :
ι → ι
.
λ x11 .
x2
(
λ x12 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x13 :
(
ι →
ι → ι
)
→ ι
.
λ x14 :
(
ι → ι
)
→
ι → ι
.
x12
(
λ x15 x16 x17 .
x2
(
λ x18 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x19 :
(
ι →
ι → ι
)
→ ι
.
λ x20 :
(
ι → ι
)
→
ι → ι
.
0
)
0
(
λ x18 x19 .
0
)
)
(
λ x15 :
ι → ι
.
Inj1
0
)
(
λ x15 .
Inj1
0
)
(
setsum
0
0
)
)
(
x0
(
λ x12 .
setsum
0
0
)
(
λ x12 .
x12
)
(
λ x12 :
(
ι → ι
)
→
ι → ι
.
λ x13 :
ι → ι
.
λ x14 .
setsum
0
0
)
(
x10
0
)
0
)
(
λ x12 x13 .
x13
)
)
(
x7
(
x3
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 :
ι → ι
.
setsum
0
0
)
0
)
)
x6
)
(
x3
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 :
ι → ι
.
x2
(
λ x13 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x14 :
(
ι →
ι → ι
)
→ ι
.
λ x15 :
(
ι → ι
)
→
ι → ι
.
x2
(
λ x16 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x17 :
(
ι →
ι → ι
)
→ ι
.
λ x18 :
(
ι → ι
)
→
ι → ι
.
0
)
(
x0
(
λ x16 .
0
)
(
λ x16 .
0
)
(
λ x16 :
(
ι → ι
)
→
ι → ι
.
λ x17 :
ι → ι
.
λ x18 .
0
)
0
0
)
(
λ x16 x17 .
x1
(
λ x18 .
0
)
0
(
λ x18 :
ι →
ι → ι
.
0
)
(
λ x18 .
0
)
)
)
(
x12
(
x1
(
λ x13 .
0
)
0
(
λ x13 :
ι →
ι → ι
.
0
)
(
λ x13 .
0
)
)
)
(
λ x13 x14 .
x1
(
λ x15 .
x13
)
(
x2
(
λ x15 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x16 :
(
ι →
ι → ι
)
→ ι
.
λ x17 :
(
ι → ι
)
→
ι → ι
.
0
)
0
(
λ x15 x16 .
0
)
)
(
λ x15 :
ι →
ι → ι
.
0
)
(
λ x15 .
0
)
)
)
0
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 x6 x7 .
x3
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 :
ι → ι
.
x2
(
λ x13 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x14 :
(
ι →
ι → ι
)
→ ι
.
λ x15 :
(
ι → ι
)
→
ι → ι
.
0
)
0
(
λ x13 x14 .
x11
(
λ x15 .
x13
)
)
)
(
setsum
(
x0
(
λ x9 .
0
)
(
λ x9 .
x5
)
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 :
ι → ι
.
λ x11 .
x7
)
0
(
x3
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 :
ι → ι
.
0
)
x6
)
)
(
x0
(
λ x9 .
0
)
(
λ x9 .
x5
)
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 :
ι → ι
.
λ x11 .
setsum
(
x2
(
λ x12 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x13 :
(
ι →
ι → ι
)
→ ι
.
λ x14 :
(
ι → ι
)
→
ι → ι
.
0
)
0
(
λ x12 x13 .
0
)
)
(
x9
(
λ x12 .
0
)
0
)
)
(
x3
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 :
ι → ι
.
x9
)
(
Inj1
0
)
)
x5
)
)
=
Inj1
(
x3
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 :
ι → ι
.
x10
)
x7
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x5 .
∀ x6 :
ι →
(
ι → ι
)
→ ι
.
∀ x7 .
x2
(
λ x9 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x10 :
(
ι →
ι → ι
)
→ ι
.
λ x11 :
(
ι → ι
)
→
ι → ι
.
Inj0
0
)
(
Inj1
(
Inj0
0
)
)
(
λ x9 x10 .
Inj1
x9
)
=
x4
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 :
ι → ι
.
λ x11 .
setsum
(
x3
(
λ x12 x13 .
λ x14 :
(
ι → ι
)
→ ι
.
λ x15 :
ι → ι
.
x2
(
λ x16 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x17 :
(
ι →
ι → ι
)
→ ι
.
λ x18 :
(
ι → ι
)
→
ι → ι
.
setsum
0
0
)
(
x1
(
λ x16 .
0
)
0
(
λ x16 :
ι →
ι → ι
.
0
)
(
λ x16 .
0
)
)
(
λ x16 x17 .
x0
(
λ x18 .
0
)
(
λ x18 .
0
)
(
λ x18 :
(
ι → ι
)
→
ι → ι
.
λ x19 :
ι → ι
.
λ x20 .
0
)
0
0
)
)
0
)
(
setsum
(
x1
(
λ x12 .
Inj1
0
)
(
Inj0
0
)
(
λ x12 :
ι →
ι → ι
.
x9
(
λ x13 .
0
)
0
)
(
λ x12 .
setsum
0
0
)
)
x7
)
)
)
⟶
(
∀ x4 .
∀ x5 :
(
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x6 :
ι → ι
.
∀ x7 :
(
ι →
ι →
ι → ι
)
→ ι
.
x2
(
λ x9 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x10 :
(
ι →
ι → ι
)
→ ι
.
λ x11 :
(
ι → ι
)
→
ι → ι
.
Inj1
0
)
(
setsum
(
x3
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 :
ι → ι
.
0
)
(
Inj1
(
x0
(
λ x9 .
0
)
(
λ x9 .
0
)
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 :
ι → ι
.
λ x11 .
0
)
0
0
)
)
)
0
)
(
λ x9 x10 .
x9
)
=
setsum
x4
0
)
⟶
(
∀ x4 .
∀ x5 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
∀ x6 x7 .
x1
(
λ x9 .
Inj1
0
)
x6
(
λ x9 :
ι →
ι → ι
.
0
)
(
λ x9 .
0
)
=
x6
)
⟶
(
∀ x4 .
∀ x5 :
ι →
ι → ι
.
∀ x6 .
∀ x7 :
ι →
ι →
ι →
ι → ι
.
x1
(
λ x9 .
Inj1
(
setsum
0
(
x5
(
Inj1
0
)
(
x1
(
λ x10 .
0
)
0
(
λ x10 :
ι →
ι → ι
.
0
)
(
λ x10 .
0
)
)
)
)
)
0
(
λ x9 :
ι →
ι → ι
.
setsum
(
x9
(
x5
(
Inj0
0
)
(
x2
(
λ x10 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x11 :
(
ι →
ι → ι
)
→ ι
.
λ x12 :
(
ι → ι
)
→
ι → ι
.
0
)
0
(
λ x10 x11 .
0
)
)
)
0
)
(
Inj0
0
)
)
(
λ x9 .
setsum
x6
(
x5
(
x1
(
λ x10 .
x0
(
λ x11 .
0
)
(
λ x11 .
0
)
(
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
0
)
0
0
)
0
(
λ x10 :
ι →
ι → ι
.
Inj0
0
)
(
λ x10 .
x0
(
λ x11 .
0
)
(
λ x11 .
0
)
(
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
0
)
0
0
)
)
0
)
)
=
Inj1
(
x3
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 :
ι → ι
.
0
)
(
x7
(
x2
(
λ x9 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x10 :
(
ι →
ι → ι
)
→ ι
.
λ x11 :
(
ι → ι
)
→
ι → ι
.
x10
(
λ x12 x13 .
0
)
)
x6
(
λ x9 x10 .
x3
(
λ x11 x12 .
λ x13 :
(
ι → ι
)
→ ι
.
λ x14 :
ι → ι
.
0
)
0
)
)
0
0
x4
)
)
)
⟶
(
∀ x4 x5 x6 x7 .
x0
(
λ x9 .
x2
(
λ x10 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x11 :
(
ι →
ι → ι
)
→ ι
.
λ x12 :
(
ι → ι
)
→
ι → ι
.
Inj0
(
Inj1
(
x1
(
λ x13 .
0
)
0
(
λ x13 :
ι →
ι → ι
.
0
)
(
λ x13 .
0
)
)
)
)
x9
(
λ x10 x11 .
x9
)
)
(
λ x9 .
Inj0
0
)
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 :
ι → ι
.
λ x11 .
Inj1
0
)
(
setsum
x7
(
setsum
(
Inj0
(
x3
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 :
ι → ι
.
0
)
0
)
)
0
)
)
(
x1
(
λ x9 .
0
)
x5
(
λ x9 :
ι →
ι → ι
.
0
)
(
λ x9 .
0
)
)
=
x2
(
λ x9 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x10 :
(
ι →
ι → ι
)
→ ι
.
λ x11 :
(
ι → ι
)
→
ι → ι
.
setsum
0
(
Inj1
0
)
)
x7
(
λ x9 x10 .
Inj1
0
)
)
⟶
(
∀ x4 x5 :
ι → ι
.
∀ x6 .
∀ x7 :
(
(
ι →
ι → ι
)
→ ι
)
→
ι → ι
.
x0
(
λ x9 .
0
)
(
λ x9 .
Inj0
x6
)
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 :
ι → ι
.
λ x11 .
0
)
0
(
x0
(
λ x9 .
0
)
(
λ x9 .
setsum
0
0
)
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 :
ι → ι
.
λ x11 .
0
)
(
x4
(
x1
(
λ x9 .
x6
)
0
(
λ x9 :
ι →
ι → ι
.
x3
(
λ x10 x11 .
λ x12 :
(
ι → ι
)
→ ι
.
λ x13 :
ι → ι
.
0
)
0
)
(
λ x9 .
x9
)
)
)
(
setsum
x6
x6
)
)
=
Inj1
(
x1
(
λ x9 .
x0
(
λ x10 .
x7
(
λ x11 :
ι →
ι → ι
.
x3
(
λ x12 x13 .
λ x14 :
(
ι → ι
)
→ ι
.
λ x15 :
ι → ι
.
0
)
0
)
(
setsum
0
0
)
)
(
λ x10 .
x9
)
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 :
ι → ι
.
x3
(
λ x12 x13 .
λ x14 :
(
ι → ι
)
→ ι
.
λ x15 :
ι → ι
.
x13
)
)
x6
x6
)
(
x5
(
setsum
(
x4
0
)
0
)
)
(
λ x9 :
ι →
ι → ι
.
0
)
(
λ x9 .
x6
)
)
)
⟶
False
(proof)
Theorem
6b7c6..
:
∀ x0 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι →
(
ι → ι
)
→ ι
)
→
ι →
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
.
∀ x1 :
(
ι → ι
)
→
ι →
ι → ι
.
∀ x2 :
(
ι →
(
(
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
(
(
(
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
.
∀ x3 :
(
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
)
→
(
(
(
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
.
(
∀ x4 .
∀ x5 :
ι →
ι →
ι →
ι → ι
.
∀ x6 .
∀ x7 :
ι → ι
.
x3
(
λ x9 :
ι →
(
ι → ι
)
→ ι
.
λ x10 .
x1
(
λ x11 .
x9
0
(
λ x12 .
setsum
0
(
x1
(
λ x13 .
0
)
0
0
)
)
)
(
x7
(
x3
(
λ x11 :
ι →
(
ι → ι
)
→ ι
.
λ x12 .
x12
)
(
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 .
λ x13 :
ι → ι
.
λ x14 .
x1
(
λ x15 .
0
)
0
0
)
)
)
(
x3
(
λ x11 :
ι →
(
ι → ι
)
→ ι
.
λ x12 .
x0
(
λ x13 :
(
ι → ι
)
→ ι
.
λ x14 x15 .
λ x16 :
ι → ι
.
Inj0
0
)
(
x2
(
λ x13 .
λ x14 :
(
ι → ι
)
→ ι
.
λ x15 :
(
ι → ι
)
→
ι → ι
.
λ x16 :
ι → ι
.
λ x17 .
0
)
(
λ x13 :
(
ι → ι
)
→ ι
.
λ x14 .
λ x15 :
ι → ι
.
0
)
0
)
(
λ x13 :
(
ι → ι
)
→ ι
.
x10
)
)
(
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 .
λ x13 :
ι → ι
.
λ x14 .
0
)
)
)
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 .
λ x11 :
ι → ι
.
λ x12 .
0
)
=
setsum
(
x5
(
x1
(
λ x9 .
x9
)
(
Inj0
0
)
(
x7
(
x1
(
λ x9 .
0
)
0
0
)
)
)
(
setsum
(
x2
(
λ x9 .
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
x3
(
λ x14 :
ι →
(
ι → ι
)
→ ι
.
λ x15 .
0
)
(
λ x14 :
(
ι → ι
)
→ ι
.
λ x15 .
λ x16 :
ι → ι
.
λ x17 .
0
)
)
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 .
λ x11 :
ι → ι
.
x9
(
λ x12 .
0
)
)
0
)
(
x5
0
0
0
(
x7
0
)
)
)
(
Inj1
(
x0
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 x11 .
λ x12 :
ι → ι
.
x1
(
λ x13 .
0
)
0
0
)
x4
(
λ x9 :
(
ι → ι
)
→ ι
.
setsum
0
0
)
)
)
(
x0
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 x11 .
λ x12 :
ι → ι
.
x12
(
x3
(
λ x13 :
ι →
(
ι → ι
)
→ ι
.
λ x14 .
0
)
(
λ x13 :
(
ι → ι
)
→ ι
.
λ x14 .
λ x15 :
ι → ι
.
λ x16 .
0
)
)
)
x4
(
λ x9 :
(
ι → ι
)
→ ι
.
x7
(
x3
(
λ x10 :
ι →
(
ι → ι
)
→ ι
.
λ x11 .
0
)
(
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 .
λ x12 :
ι → ι
.
λ x13 .
0
)
)
)
)
)
0
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 .
∀ x6 :
ι →
ι → ι
.
∀ x7 :
(
ι → ι
)
→ ι
.
x3
(
λ x9 :
ι →
(
ι → ι
)
→ ι
.
λ x10 .
setsum
(
x7
(
λ x11 .
x9
x10
(
λ x12 .
Inj0
0
)
)
)
(
setsum
(
x1
(
λ x11 .
0
)
(
Inj1
0
)
0
)
0
)
)
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 .
λ x11 :
ι → ι
.
Inj1
)
=
setsum
(
x1
(
λ x9 .
x7
(
λ x10 .
Inj0
0
)
)
(
x6
0
(
x4
0
)
)
(
x7
(
λ x9 .
x3
(
λ x10 :
ι →
(
ι → ι
)
→ ι
.
λ x11 .
0
)
(
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 .
λ x12 :
ι → ι
.
λ x13 .
0
)
)
)
)
(
x0
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 x11 .
λ x12 :
ι → ι
.
x10
)
(
x0
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 x11 .
λ x12 :
ι → ι
.
Inj0
(
x3
(
λ x13 :
ι →
(
ι → ι
)
→ ι
.
λ x14 .
0
)
(
λ x13 :
(
ι → ι
)
→ ι
.
λ x14 .
λ x15 :
ι → ι
.
λ x16 .
0
)
)
)
(
x7
(
λ x9 .
x7
(
λ x10 .
0
)
)
)
(
λ x9 :
(
ι → ι
)
→ ι
.
0
)
)
(
λ x9 :
(
ι → ι
)
→ ι
.
x0
(
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 x12 .
λ x13 :
ι → ι
.
setsum
(
x0
(
λ x14 :
(
ι → ι
)
→ ι
.
λ x15 x16 .
λ x17 :
ι → ι
.
0
)
0
(
λ x14 :
(
ι → ι
)
→ ι
.
0
)
)
(
x13
0
)
)
0
(
λ x10 :
(
ι → ι
)
→ ι
.
x10
(
λ x11 .
x0
(
λ x12 :
(
ι → ι
)
→ ι
.
λ x13 x14 .
λ x15 :
ι → ι
.
0
)
0
(
λ x12 :
(
ι → ι
)
→ ι
.
0
)
)
)
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 :
ι →
ι → ι
.
∀ x6 :
ι → ι
.
∀ x7 :
ι →
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
x2
(
λ x9 .
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
0
)
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 .
λ x11 :
ι → ι
.
x10
)
(
setsum
(
Inj1
(
x2
(
λ x9 .
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
0
)
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 .
λ x11 :
ι → ι
.
x3
(
λ x12 :
ι →
(
ι → ι
)
→ ι
.
λ x13 .
0
)
(
λ x12 :
(
ι → ι
)
→ ι
.
λ x13 .
λ x14 :
ι → ι
.
λ x15 .
0
)
)
(
x4
0
)
)
)
0
)
=
x5
(
x2
(
λ x9 .
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
0
)
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 .
λ x11 :
ι → ι
.
0
)
0
)
(
setsum
(
Inj0
0
)
(
Inj0
(
Inj1
(
x7
0
(
λ x9 :
ι → ι
.
0
)
0
0
)
)
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 .
∀ x6 :
ι → ι
.
∀ x7 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
x2
(
λ x9 .
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
x0
(
λ x14 :
(
ι → ι
)
→ ι
.
λ x15 x16 .
λ x17 :
ι → ι
.
x14
(
λ x18 .
0
)
)
(
x1
(
λ x14 .
0
)
x13
0
)
(
λ x14 :
(
ι → ι
)
→ ι
.
setsum
(
setsum
(
setsum
0
0
)
(
x11
(
λ x15 .
0
)
0
)
)
0
)
)
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 .
λ x11 :
ι → ι
.
x11
(
x11
(
x11
0
)
)
)
(
x2
(
λ x9 .
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
Inj0
(
x11
(
λ x14 .
x11
(
λ x15 .
0
)
0
)
(
x3
(
λ x14 :
ι →
(
ι → ι
)
→ ι
.
λ x15 .
0
)
(
λ x14 :
(
ι → ι
)
→ ι
.
λ x15 .
λ x16 :
ι → ι
.
λ x17 .
0
)
)
)
)
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 .
λ x11 :
ι → ι
.
x2
(
λ x12 .
λ x13 :
(
ι → ι
)
→ ι
.
λ x14 :
(
ι → ι
)
→
ι → ι
.
λ x15 :
ι → ι
.
λ x16 .
Inj0
(
x14
(
λ x17 .
0
)
0
)
)
(
λ x12 :
(
ι → ι
)
→ ι
.
λ x13 .
λ x14 :
ι → ι
.
x1
(
λ x15 .
x2
(
λ x16 .
λ x17 :
(
ι → ι
)
→ ι
.
λ x18 :
(
ι → ι
)
→
ι → ι
.
λ x19 :
ι → ι
.
λ x20 .
0
)
(
λ x16 :
(
ι → ι
)
→ ι
.
λ x17 .
λ x18 :
ι → ι
.
0
)
0
)
(
x3
(
λ x15 :
ι →
(
ι → ι
)
→ ι
.
λ x16 .
0
)
(
λ x15 :
(
ι → ι
)
→ ι
.
λ x16 .
λ x17 :
ι → ι
.
λ x18 .
0
)
)
(
x0
(
λ x15 :
(
ι → ι
)
→ ι
.
λ x16 x17 .
λ x18 :
ι → ι
.
0
)
0
(
λ x15 :
(
ι → ι
)
→ ι
.
0
)
)
)
(
x1
(
λ x12 .
0
)
(
x1
(
λ x12 .
0
)
0
0
)
(
x0
(
λ x12 :
(
ι → ι
)
→ ι
.
λ x13 x14 .
λ x15 :
ι → ι
.
0
)
0
(
λ x12 :
(
ι → ι
)
→ ι
.
0
)
)
)
)
(
x7
0
(
λ x9 :
ι → ι
.
x5
)
)
)
=
setsum
(
x6
(
x2
(
λ x9 .
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
0
)
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 .
λ x11 :
ι → ι
.
x3
(
λ x12 :
ι →
(
ι → ι
)
→ ι
.
λ x13 .
setsum
0
0
)
(
λ x12 :
(
ι → ι
)
→ ι
.
λ x13 .
λ x14 :
ι → ι
.
λ x15 .
x1
(
λ x16 .
0
)
0
0
)
)
(
x1
(
λ x9 .
x1
(
λ x10 .
0
)
0
0
)
(
x2
(
λ x9 .
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
0
)
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 .
λ x11 :
ι → ι
.
0
)
0
)
(
x4
0
)
)
)
)
0
)
⟶
(
∀ x4 .
∀ x5 :
(
(
ι →
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x6 :
ι → ι
.
∀ x7 .
x1
(
λ x9 .
x9
)
(
x1
(
λ x9 .
x9
)
(
Inj0
(
setsum
(
Inj1
0
)
(
x1
(
λ x9 .
0
)
0
0
)
)
)
x4
)
x7
=
x7
)
⟶
(
∀ x4 :
(
ι → ι
)
→
ι →
(
ι → ι
)
→ ι
.
∀ x5 :
ι →
ι → ι
.
∀ x6 :
ι →
ι →
(
ι → ι
)
→ ι
.
∀ x7 .
x1
(
λ x9 .
setsum
(
x0
(
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 x12 .
λ x13 :
ι → ι
.
x1
(
λ x14 .
x3
(
λ x15 :
ι →
(
ι → ι
)
→ ι
.
λ x16 .
0
)
(
λ x15 :
(
ι → ι
)
→ ι
.
λ x16 .
λ x17 :
ι → ι
.
λ x18 .
0
)
)
(
setsum
0
0
)
0
)
x9
(
λ x10 :
(
ι → ι
)
→ ι
.
0
)
)
0
)
(
x5
0
(
x4
(
λ x9 .
0
)
(
x2
(
λ x9 .
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
x0
(
λ x14 :
(
ι → ι
)
→ ι
.
λ x15 x16 .
λ x17 :
ι → ι
.
0
)
0
(
λ x14 :
(
ι → ι
)
→ ι
.
0
)
)
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 .
λ x11 :
ι → ι
.
setsum
0
0
)
0
)
(
λ x9 .
x2
(
λ x10 .
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 :
(
ι → ι
)
→
ι → ι
.
λ x13 :
ι → ι
.
λ x14 .
x3
(
λ x15 :
ι →
(
ι → ι
)
→ ι
.
λ x16 .
0
)
(
λ x15 :
(
ι → ι
)
→ ι
.
λ x16 .
λ x17 :
ι → ι
.
λ x18 .
0
)
)
(
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 .
λ x12 :
ι → ι
.
setsum
0
0
)
(
Inj1
0
)
)
)
)
(
x0
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 x11 .
λ x12 :
ι → ι
.
x2
(
λ x13 .
λ x14 :
(
ι → ι
)
→ ι
.
λ x15 :
(
ι → ι
)
→
ι → ι
.
λ x16 :
ι → ι
.
λ x17 .
Inj1
(
x3
(
λ x18 :
ι →
(
ι → ι
)
→ ι
.
λ x19 .
0
)
(
λ x18 :
(
ι → ι
)
→ ι
.
λ x19 .
λ x20 :
ι → ι
.
λ x21 .
0
)
)
)
(
λ x13 :
(
ι → ι
)
→ ι
.
λ x14 .
λ x15 :
ι → ι
.
x12
(
x3
(
λ x16 :
ι →
(
ι → ι
)
→ ι
.
λ x17 .
0
)
(
λ x16 :
(
ι → ι
)
→ ι
.
λ x17 .
λ x18 :
ι → ι
.
λ x19 .
0
)
)
)
x11
)
x7
(
λ x9 :
(
ι → ι
)
→ ι
.
x1
(
λ x10 .
x0
(
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 x13 .
λ x14 :
ι → ι
.
0
)
(
x2
(
λ x11 .
λ x12 :
(
ι → ι
)
→ ι
.
λ x13 :
(
ι → ι
)
→
ι → ι
.
λ x14 :
ι → ι
.
λ x15 .
0
)
(
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 .
λ x13 :
ι → ι
.
0
)
0
)
(
λ x11 :
(
ι → ι
)
→ ι
.
Inj1
0
)
)
(
x5
(
x9
(
λ x10 .
0
)
)
(
x6
0
0
(
λ x10 .
0
)
)
)
0
)
)
=
setsum
(
Inj1
(
x2
(
λ x9 .
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
x3
(
λ x14 :
ι →
(
ι → ι
)
→ ι
.
λ x15 .
x12
0
)
(
λ x14 :
(
ι → ι
)
→ ι
.
λ x15 .
λ x16 :
ι → ι
.
λ x17 .
x17
)
)
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 .
λ x11 :
ι → ι
.
x1
(
λ x12 .
0
)
(
x3
(
λ x12 :
ι →
(
ι → ι
)
→ ι
.
λ x13 .
0
)
(
λ x12 :
(
ι → ι
)
→ ι
.
λ x13 .
λ x14 :
ι → ι
.
λ x15 .
0
)
)
(
setsum
0
0
)
)
0
)
)
(
Inj1
(
x5
x7
(
Inj0
0
)
)
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
∀ x5 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x6 .
∀ x7 :
(
(
ι →
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
x0
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 x11 .
λ x12 :
ι → ι
.
x10
)
(
x1
(
λ x9 .
x0
(
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 x12 .
λ x13 :
ι → ι
.
x11
)
(
x7
(
λ x10 :
ι →
ι → ι
.
x7
(
λ x11 :
ι →
ι → ι
.
0
)
(
λ x11 .
0
)
(
λ x11 .
0
)
)
(
λ x10 .
x2
(
λ x11 .
λ x12 :
(
ι → ι
)
→ ι
.
λ x13 :
(
ι → ι
)
→
ι → ι
.
λ x14 :
ι → ι
.
λ x15 .
0
)
(
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 .
λ x13 :
ι → ι
.
0
)
0
)
(
λ x10 .
x1
(
λ x11 .
0
)
0
0
)
)
(
λ x10 :
(
ι → ι
)
→ ι
.
setsum
x9
(
setsum
0
0
)
)
)
(
setsum
(
x0
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 x11 .
λ x12 :
ι → ι
.
x10
)
(
Inj0
0
)
(
λ x9 :
(
ι → ι
)
→ ι
.
x3
(
λ x10 :
ι →
(
ι → ι
)
→ ι
.
λ x11 .
0
)
(
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 .
λ x12 :
ι → ι
.
λ x13 .
0
)
)
)
(
x4
(
λ x9 .
Inj0
0
)
(
setsum
0
0
)
(
λ x9 .
x9
)
(
x7
(
λ x9 :
ι →
ι → ι
.
0
)
(
λ x9 .
0
)
(
λ x9 .
0
)
)
)
)
0
)
(
λ x9 :
(
ι → ι
)
→ ι
.
Inj1
x6
)
=
x1
(
λ x9 .
x1
(
λ x10 .
x1
(
λ x11 .
0
)
(
x2
(
λ x11 .
λ x12 :
(
ι → ι
)
→ ι
.
λ x13 :
(
ι → ι
)
→
ι → ι
.
λ x14 :
ι → ι
.
λ x15 .
x2
(
λ x16 .
λ x17 :
(
ι → ι
)
→ ι
.
λ x18 :
(
ι → ι
)
→
ι → ι
.
λ x19 :
ι → ι
.
λ x20 .
0
)
(
λ x16 :
(
ι → ι
)
→ ι
.
λ x17 .
λ x18 :
ι → ι
.
0
)
0
)
(
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 .
λ x13 :
ι → ι
.
Inj1
0
)
0
)
0
)
(
x5
0
(
λ x10 :
ι → ι
.
λ x11 .
0
)
)
0
)
(
x1
(
λ x9 .
0
)
(
x7
(
λ x9 :
ι →
ι → ι
.
0
)
(
λ x9 .
0
)
(
λ x9 .
setsum
0
0
)
)
(
Inj1
(
Inj0
(
x4
(
λ x9 .
0
)
0
(
λ x9 .
0
)
0
)
)
)
)
x6
)
⟶
(
∀ x4 x5 :
ι → ι
.
∀ x6 x7 .
x0
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 x11 .
λ x12 :
ι → ι
.
0
)
(
x1
(
λ x9 .
0
)
x7
(
x4
(
x0
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 x11 .
λ x12 :
ι → ι
.
x10
)
0
(
λ x9 :
(
ι → ι
)
→ ι
.
x2
(
λ x10 .
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 :
(
ι → ι
)
→
ι → ι
.
λ x13 :
ι → ι
.
λ x14 .
0
)
(
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 .
λ x12 :
ι → ι
.
0
)
0
)
)
)
)
(
λ x9 :
(
ι → ι
)
→ ι
.
0
)
=
x1
(
λ x9 .
x2
(
λ x10 .
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 :
(
ι → ι
)
→
ι → ι
.
λ x13 :
ι → ι
.
λ x14 .
Inj1
(
x12
(
λ x15 .
x2
(
λ x16 .
λ x17 :
(
ι → ι
)
→ ι
.
λ x18 :
(
ι → ι
)
→
ι → ι
.
λ x19 :
ι → ι
.
λ x20 .
0
)
(
λ x16 :
(
ι → ι
)
→ ι
.
λ x17 .
λ x18 :
ι → ι
.
0
)
0
)
(
setsum
0
0
)
)
)
(
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 .
λ x12 :
ι → ι
.
0
)
(
x3
(
λ x10 :
ι →
(
ι → ι
)
→ ι
.
λ x11 .
x9
)
(
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 .
λ x12 :
ι → ι
.
λ x13 .
0
)
)
)
(
Inj0
(
x0
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 x11 .
λ x12 :
ι → ι
.
x11
)
x7
(
λ x9 :
(
ι → ι
)
→ ι
.
x9
(
λ x10 .
0
)
)
)
)
(
setsum
(
setsum
(
Inj0
0
)
(
setsum
x6
0
)
)
0
)
)
⟶
False
(proof)
Theorem
c772a..
:
∀ x0 :
(
ι →
ι →
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
(
(
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
∀ x1 :
(
ι →
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι → ι
.
∀ x2 :
(
(
ι →
(
ι →
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι →
ι →
ι → ι
)
→
ι → ι
.
∀ x3 :
(
(
ι →
ι →
ι →
ι → ι
)
→
(
ι →
ι →
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
)
→
ι →
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
)
→
ι → ι
.
(
∀ x4 :
(
ι →
ι → ι
)
→
ι → ι
.
∀ x5 .
∀ x6 :
(
ι → ι
)
→
ι →
ι → ι
.
∀ x7 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
x3
(
λ x9 :
ι →
ι →
ι →
ι → ι
.
λ x10 :
ι →
ι →
ι → ι
.
λ x11 .
λ x12 :
ι → ι
.
λ x13 .
0
)
(
x4
(
λ x9 x10 .
Inj1
0
)
(
Inj1
(
setsum
(
x7
(
λ x9 :
ι →
ι → ι
.
λ x10 :
ι → ι
.
0
)
0
0
)
0
)
)
)
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
0
)
(
x1
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→
ι → ι
.
x2
(
λ x12 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x13 :
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x14 x15 x16 .
0
)
(
x3
(
λ x12 :
ι →
ι →
ι →
ι → ι
.
λ x13 :
ι →
ι →
ι → ι
.
λ x14 .
λ x15 :
ι → ι
.
λ x16 .
x3
(
λ x17 :
ι →
ι →
ι →
ι → ι
.
λ x18 :
ι →
ι →
ι → ι
.
λ x19 .
λ x20 :
ι → ι
.
λ x21 .
0
)
0
(
λ x17 :
(
ι → ι
)
→ ι
.
λ x18 :
ι → ι
.
0
)
0
)
x9
(
λ x12 :
(
ι → ι
)
→ ι
.
λ x13 :
ι → ι
.
x11
(
λ x14 .
0
)
0
)
(
setsum
0
0
)
)
)
(
Inj0
0
)
)
=
setsum
(
x0
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→ ι
.
0
)
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι →
ι → ι
.
λ x11 :
ι → ι
.
λ x12 .
0
)
(
x4
(
λ x9 x10 .
0
)
0
)
)
x5
)
⟶
(
∀ x4 :
ι →
(
ι →
ι → ι
)
→ ι
.
∀ x5 :
ι →
(
ι → ι
)
→ ι
.
∀ x6 .
∀ x7 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
.
x3
(
λ x9 :
ι →
ι →
ι →
ι → ι
.
λ x10 :
ι →
ι →
ι → ι
.
λ x11 .
λ x12 :
ι → ι
.
λ x13 .
x12
(
x0
(
λ x14 x15 .
λ x16 :
(
ι → ι
)
→ ι
.
x2
(
λ x17 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x18 :
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x19 x20 x21 .
setsum
0
0
)
0
)
(
λ x14 :
(
ι → ι
)
→ ι
.
λ x15 :
ι →
ι → ι
.
λ x16 :
ι → ι
.
λ x17 .
setsum
(
x14
(
λ x18 .
0
)
)
(
Inj0
0
)
)
0
)
)
(
Inj1
0
)
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
setsum
x6
(
setsum
0
(
x0
(
λ x11 x12 .
λ x13 :
(
ι → ι
)
→ ι
.
x2
(
λ x14 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x15 :
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x16 x17 x18 .
0
)
0
)
(
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 :
ι →
ι → ι
.
λ x13 :
ι → ι
.
λ x14 .
x12
0
0
)
(
x3
(
λ x11 :
ι →
ι →
ι →
ι → ι
.
λ x12 :
ι →
ι →
ι → ι
.
λ x13 .
λ x14 :
ι → ι
.
λ x15 .
0
)
0
(
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 :
ι → ι
.
0
)
0
)
)
)
)
(
x7
(
λ x9 :
(
ι → ι
)
→ ι
.
x9
(
λ x10 .
x9
(
λ x11 .
0
)
)
)
)
=
x7
(
λ x9 :
(
ι → ι
)
→ ι
.
setsum
0
(
x3
(
λ x10 :
ι →
ι →
ι →
ι → ι
.
λ x11 :
ι →
ι →
ι → ι
.
λ x12 .
λ x13 :
ι → ι
.
λ x14 .
x13
(
x11
0
0
0
)
)
0
(
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 :
ι → ι
.
x1
(
λ x12 x13 .
λ x14 :
(
ι → ι
)
→
ι → ι
.
x14
(
λ x15 .
0
)
0
)
(
x10
(
λ x12 .
0
)
)
)
(
x5
x6
(
λ x10 .
x6
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
(
ι → ι
)
→ ι
.
∀ x6 x7 .
x2
(
λ x9 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x10 :
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x11 x12 x13 .
setsum
(
x1
(
λ x14 x15 .
λ x16 :
(
ι → ι
)
→
ι → ι
.
setsum
(
x16
(
λ x17 .
0
)
0
)
(
Inj1
0
)
)
(
Inj0
(
x3
(
λ x14 :
ι →
ι →
ι →
ι → ι
.
λ x15 :
ι →
ι →
ι → ι
.
λ x16 .
λ x17 :
ι → ι
.
λ x18 .
0
)
0
(
λ x14 :
(
ι → ι
)
→ ι
.
λ x15 :
ι → ι
.
0
)
0
)
)
)
(
x1
(
λ x14 x15 .
λ x16 :
(
ι → ι
)
→
ι → ι
.
x14
)
0
)
)
(
setsum
(
setsum
(
Inj0
0
)
0
)
(
x0
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→ ι
.
x0
(
λ x12 x13 .
λ x14 :
(
ι → ι
)
→ ι
.
setsum
0
0
)
(
λ x12 :
(
ι → ι
)
→ ι
.
λ x13 :
ι →
ι → ι
.
λ x14 :
ι → ι
.
λ x15 .
Inj0
0
)
0
)
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι →
ι → ι
.
λ x11 :
ι → ι
.
λ x12 .
x9
(
λ x13 .
x10
0
0
)
)
(
x2
(
λ x9 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x10 :
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x11 x12 x13 .
setsum
0
0
)
(
x2
(
λ x9 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x10 :
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x11 x12 x13 .
0
)
0
)
)
)
)
=
x6
)
⟶
(
∀ x4 x5 x6 x7 .
x2
(
λ x9 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x10 :
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x11 x12 x13 .
x0
(
λ x14 x15 .
λ x16 :
(
ι → ι
)
→ ι
.
x14
)
(
λ x14 :
(
ι → ι
)
→ ι
.
λ x15 :
ι →
ι → ι
.
λ x16 :
ι → ι
.
λ x17 .
0
)
(
Inj1
(
x2
(
λ x14 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x15 :
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x16 x17 x18 .
x16
)
x13
)
)
)
(
x2
(
λ x9 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x10 :
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x11 x12 x13 .
x2
(
λ x14 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x15 :
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x16 x17 x18 .
x1
(
λ x19 x20 .
λ x21 :
(
ι → ι
)
→
ι → ι
.
x0
(
λ x22 x23 .
λ x24 :
(
ι → ι
)
→ ι
.
0
)
(
λ x22 :
(
ι → ι
)
→ ι
.
λ x23 :
ι →
ι → ι
.
λ x24 :
ι → ι
.
λ x25 .
0
)
0
)
(
x1
(
λ x19 x20 .
λ x21 :
(
ι → ι
)
→
ι → ι
.
0
)
0
)
)
(
setsum
(
x3
(
λ x14 :
ι →
ι →
ι →
ι → ι
.
λ x15 :
ι →
ι →
ι → ι
.
λ x16 .
λ x17 :
ι → ι
.
λ x18 .
0
)
0
(
λ x14 :
(
ι → ι
)
→ ι
.
λ x15 :
ι → ι
.
0
)
0
)
0
)
)
(
x2
(
λ x9 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x10 :
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x11 x12 x13 .
x3
(
λ x14 :
ι →
ι →
ι →
ι → ι
.
λ x15 :
ι →
ι →
ι → ι
.
λ x16 .
λ x17 :
ι → ι
.
λ x18 .
x0
(
λ x19 x20 .
λ x21 :
(
ι → ι
)
→ ι
.
0
)
(
λ x19 :
(
ι → ι
)
→ ι
.
λ x20 :
ι →
ι → ι
.
λ x21 :
ι → ι
.
λ x22 .
0
)
0
)
(
x3
(
λ x14 :
ι →
ι →
ι →
ι → ι
.
λ x15 :
ι →
ι →
ι → ι
.
λ x16 .
λ x17 :
ι → ι
.
λ x18 .
0
)
0
(
λ x14 :
(
ι → ι
)
→ ι
.
λ x15 :
ι → ι
.
0
)
0
)
(
λ x14 :
(
ι → ι
)
→ ι
.
λ x15 :
ι → ι
.
0
)
(
setsum
0
0
)
)
(
Inj0
(
setsum
0
0
)
)
)
)
=
Inj0
(
setsum
x6
(
x1
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→
ι → ι
.
0
)
0
)
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x6 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
.
∀ x7 :
(
(
ι →
ι → ι
)
→
ι → ι
)
→ ι
.
x1
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→
ι → ι
.
0
)
0
=
Inj1
(
x0
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→ ι
.
x1
(
λ x12 x13 .
λ x14 :
(
ι → ι
)
→
ι → ι
.
0
)
(
Inj1
x10
)
)
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι →
ι → ι
.
λ x11 :
ι → ι
.
λ x12 .
Inj1
(
x10
0
(
x1
(
λ x13 x14 .
λ x15 :
(
ι → ι
)
→
ι → ι
.
0
)
0
)
)
)
x4
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→ ι
.
∀ x5 .
∀ x6 :
ι →
ι →
(
ι → ι
)
→
ι → ι
.
∀ x7 :
(
(
ι →
ι → ι
)
→
ι → ι
)
→ ι
.
x1
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→
ι → ι
.
x3
(
λ x12 :
ι →
ι →
ι →
ι → ι
.
λ x13 :
ι →
ι →
ι → ι
.
λ x14 .
λ x15 :
ι → ι
.
λ x16 .
x0
(
λ x17 x18 .
λ x19 :
(
ι → ι
)
→ ι
.
Inj0
(
setsum
0
0
)
)
(
λ x17 :
(
ι → ι
)
→ ι
.
λ x18 :
ι →
ι → ι
.
λ x19 :
ι → ι
.
λ x20 .
Inj0
(
setsum
0
0
)
)
(
x15
(
setsum
0
0
)
)
)
(
x2
(
λ x12 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x13 :
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x14 x15 x16 .
setsum
(
setsum
0
0
)
x14
)
(
setsum
(
x11
(
λ x12 .
0
)
0
)
(
x1
(
λ x12 x13 .
λ x14 :
(
ι → ι
)
→
ι → ι
.
0
)
0
)
)
)
(
λ x12 :
(
ι → ι
)
→ ι
.
λ x13 :
ι → ι
.
setsum
0
(
Inj0
(
setsum
0
0
)
)
)
0
)
(
x6
(
Inj0
(
x4
(
λ x9 .
0
)
)
)
(
setsum
0
0
)
(
λ x9 .
x5
)
(
x6
(
x4
(
λ x9 .
setsum
0
0
)
)
(
x7
(
λ x9 :
ι →
ι → ι
.
λ x10 .
x6
0
0
(
λ x11 .
0
)
0
)
)
(
λ x9 .
setsum
(
setsum
0
0
)
0
)
(
Inj0
0
)
)
)
=
x6
(
x0
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→ ι
.
x0
(
λ x12 x13 .
λ x14 :
(
ι → ι
)
→ ι
.
Inj0
(
x0
(
λ x15 x16 .
λ x17 :
(
ι → ι
)
→ ι
.
0
)
(
λ x15 :
(
ι → ι
)
→ ι
.
λ x16 :
ι →
ι → ι
.
λ x17 :
ι → ι
.
λ x18 .
0
)
0
)
)
(
λ x12 :
(
ι → ι
)
→ ι
.
λ x13 :
ι →
ι → ι
.
λ x14 :
ι → ι
.
λ x15 .
x13
0
(
Inj0
0
)
)
(
Inj1
(
Inj0
0
)
)
)
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι →
ι → ι
.
λ x11 :
ι → ι
.
λ x12 .
0
)
(
x0
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→ ι
.
0
)
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι →
ι → ι
.
λ x11 :
ι → ι
.
λ x12 .
0
)
0
)
)
(
x0
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→ ι
.
x2
(
λ x12 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x13 :
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x14 x15 x16 .
x15
)
(
x3
(
λ x12 :
ι →
ι →
ι →
ι → ι
.
λ x13 :
ι →
ι →
ι → ι
.
λ x14 .
λ x15 :
ι → ι
.
λ x16 .
x13
0
0
0
)
(
x11
(
λ x12 .
0
)
)
(
λ x12 :
(
ι → ι
)
→ ι
.
λ x13 :
ι → ι
.
0
)
(
Inj1
0
)
)
)
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι →
ι → ι
.
λ x11 :
ι → ι
.
λ x12 .
x0
(
λ x13 x14 .
λ x15 :
(
ι → ι
)
→ ι
.
setsum
0
(
Inj1
0
)
)
(
λ x13 :
(
ι → ι
)
→ ι
.
λ x14 :
ι →
ι → ι
.
λ x15 :
ι → ι
.
λ x16 .
x16
)
(
x1
(
λ x13 x14 .
λ x15 :
(
ι → ι
)
→
ι → ι
.
0
)
(
x9
(
λ x13 .
0
)
)
)
)
(
x4
(
λ x9 .
x6
(
x2
(
λ x10 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x11 :
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x12 x13 x14 .
0
)
0
)
0
(
λ x10 .
x3
(
λ x11 :
ι →
ι →
ι →
ι → ι
.
λ x12 :
ι →
ι →
ι → ι
.
λ x13 .
λ x14 :
ι → ι
.
λ x15 .
0
)
0
(
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 :
ι → ι
.
0
)
0
)
0
)
)
)
(
λ x9 .
Inj0
(
Inj0
0
)
)
(
x0
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→ ι
.
x7
(
λ x12 :
ι →
ι → ι
.
λ x13 .
setsum
(
x3
(
λ x14 :
ι →
ι →
ι →
ι → ι
.
λ x15 :
ι →
ι →
ι → ι
.
λ x16 .
λ x17 :
ι → ι
.
λ x18 .
0
)
0
(
λ x14 :
(
ι → ι
)
→ ι
.
λ x15 :
ι → ι
.
0
)
0
)
(
setsum
0
0
)
)
)
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι →
ι → ι
.
λ x11 :
ι → ι
.
λ x12 .
setsum
(
x3
(
λ x13 :
ι →
ι →
ι →
ι → ι
.
λ x14 :
ι →
ι →
ι → ι
.
λ x15 .
λ x16 :
ι → ι
.
λ x17 .
0
)
(
Inj0
0
)
(
λ x13 :
(
ι → ι
)
→ ι
.
λ x14 :
ι → ι
.
Inj1
0
)
(
Inj1
0
)
)
(
setsum
(
Inj0
0
)
(
x11
0
)
)
)
(
x3
(
λ x9 :
ι →
ι →
ι →
ι → ι
.
λ x10 :
ι →
ι →
ι → ι
.
λ x11 .
λ x12 :
ι → ι
.
λ x13 .
0
)
(
x3
(
λ x9 :
ι →
ι →
ι →
ι → ι
.
λ x10 :
ι →
ι →
ι → ι
.
λ x11 .
λ x12 :
ι → ι
.
λ x13 .
x13
)
(
x4
(
λ x9 .
0
)
)
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
setsum
0
0
)
(
x1
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→
ι → ι
.
0
)
0
)
)
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
0
)
(
Inj1
(
x4
(
λ x9 .
0
)
)
)
)
)
)
⟶
(
∀ x4 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x5 :
ι → ι
.
∀ x6 :
ι →
ι →
(
ι → ι
)
→ ι
.
∀ x7 .
x0
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→ ι
.
x11
(
λ x12 .
x2
(
λ x13 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x14 :
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x15 x16 .
setsum
0
)
(
Inj0
x10
)
)
)
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι →
ι → ι
.
λ x11 :
ι → ι
.
λ x12 .
0
)
(
Inj1
(
setsum
0
(
x5
(
setsum
0
0
)
)
)
)
=
x5
0
)
⟶
(
∀ x4 x5 .
∀ x6 :
ι → ι
.
∀ x7 .
x0
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→ ι
.
x1
(
λ x12 x13 .
λ x14 :
(
ι → ι
)
→
ι → ι
.
x12
)
(
x1
(
λ x12 x13 .
λ x14 :
(
ι → ι
)
→
ι → ι
.
0
)
(
x11
(
λ x12 .
x9
)
)
)
)
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι →
ι → ι
.
λ x11 :
ι → ι
.
λ x12 .
setsum
0
(
setsum
(
Inj0
(
setsum
0
0
)
)
(
x0
(
λ x13 x14 .
λ x15 :
(
ι → ι
)
→ ι
.
Inj0
0
)
(
λ x13 :
(
ι → ι
)
→ ι
.
λ x14 :
ι →
ι → ι
.
λ x15 :
ι → ι
.
λ x16 .
0
)
(
Inj0
0
)
)
)
)
(
x1
(
λ x9 x10 .
λ x11 :
(
ι → ι
)
→
ι → ι
.
0
)
(
Inj1
(
x6
x4
)
)
)
=
setsum
x7
0
)
⟶
False
(proof)
Theorem
b4427..
:
∀ x0 :
(
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
)
→
ι →
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
∀ x1 x2 :
(
ι → ι
)
→
ι → ι
.
∀ x3 :
(
ι →
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι →
ι →
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
(
∀ x4 x5 .
∀ x6 :
ι → ι
.
∀ x7 .
x3
(
λ x9 .
λ x10 :
ι →
(
ι → ι
)
→
ι → ι
.
x6
(
x0
(
λ x11 :
(
(
ι → ι
)
→ ι
)
→ ι
.
Inj1
0
)
0
(
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 :
ι → ι
.
λ x13 .
Inj0
(
setsum
0
0
)
)
0
)
)
(
Inj0
0
)
(
x1
(
λ x9 .
x2
(
λ x10 .
Inj0
0
)
(
x3
(
λ x10 .
λ x11 :
ι →
(
ι → ι
)
→
ι → ι
.
x2
(
λ x12 .
0
)
0
)
(
x1
(
λ x10 .
0
)
0
)
x9
(
λ x10 :
ι → ι
.
0
)
(
λ x10 .
Inj1
0
)
(
x2
(
λ x10 .
0
)
0
)
)
)
x5
)
(
λ x9 :
ι → ι
.
Inj0
x5
)
(
λ x9 .
Inj0
(
Inj0
(
x2
(
λ x10 .
Inj1
0
)
0
)
)
)
(
setsum
x5
x7
)
=
setsum
(
Inj1
(
x6
(
Inj0
(
setsum
0
0
)
)
)
)
x7
)
⟶
(
∀ x4 .
∀ x5 :
(
ι → ι
)
→ ι
.
∀ x6 x7 .
x3
(
λ x9 .
λ x10 :
ι →
(
ι → ι
)
→
ι → ι
.
setsum
(
x3
(
λ x11 .
λ x12 :
ι →
(
ι → ι
)
→
ι → ι
.
x3
(
λ x13 .
λ x14 :
ι →
(
ι → ι
)
→
ι → ι
.
0
)
0
x9
(
λ x13 :
ι → ι
.
x10
0
(
λ x14 .
0
)
0
)
(
λ x13 .
x12
0
(
λ x14 .
0
)
0
)
x11
)
(
x2
(
λ x11 .
x3
(
λ x12 .
λ x13 :
ι →
(
ι → ι
)
→
ι → ι
.
0
)
0
0
(
λ x12 :
ι → ι
.
0
)
(
λ x12 .
0
)
0
)
(
x3
(
λ x11 .
λ x12 :
ι →
(
ι → ι
)
→
ι → ι
.
0
)
0
0
(
λ x11 :
ι → ι
.
0
)
(
λ x11 .
0
)
0
)
)
x6
(
λ x11 :
ι → ι
.
x0
(
λ x12 :
(
(
ι → ι
)
→ ι
)
→ ι
.
x9
)
0
(
λ x12 :
(
ι → ι
)
→ ι
.
λ x13 :
ι → ι
.
λ x14 .
x11
0
)
(
Inj1
0
)
)
(
λ x11 .
x11
)
(
setsum
(
x1
(
λ x11 .
0
)
0
)
(
x0
(
λ x11 :
(
(
ι → ι
)
→ ι
)
→ ι
.
0
)
0
(
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 :
ι → ι
.
λ x13 .
0
)
0
)
)
)
0
)
x7
x4
(
λ x9 :
ι → ι
.
Inj0
0
)
(
λ x9 .
x1
(
λ x10 .
x6
)
(
x3
(
λ x10 .
λ x11 :
ι →
(
ι → ι
)
→
ι → ι
.
setsum
x9
0
)
(
x0
(
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
0
)
(
x2
(
λ x10 .
0
)
0
)
(
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 :
ι → ι
.
λ x12 .
x3
(
λ x13 .
λ x14 :
ι →
(
ι → ι
)
→
ι → ι
.
0
)
0
0
(
λ x13 :
ι → ι
.
0
)
(
λ x13 .
0
)
0
)
(
x2
(
λ x10 .
0
)
0
)
)
(
x5
(
λ x10 .
x0
(
λ x11 :
(
(
ι → ι
)
→ ι
)
→ ι
.
0
)
0
(
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 :
ι → ι
.
λ x13 .
0
)
0
)
)
(
λ x10 :
ι → ι
.
0
)
(
λ x10 .
0
)
x7
)
)
0
=
x1
(
λ x9 .
x9
)
(
x1
(
λ x9 .
x9
)
(
setsum
(
x3
(
λ x9 .
λ x10 :
ι →
(
ι → ι
)
→
ι → ι
.
Inj0
0
)
x6
0
(
λ x9 :
ι → ι
.
Inj1
0
)
(
λ x9 .
x1
(
λ x10 .
0
)
0
)
0
)
x7
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 .
∀ x6 :
ι → ι
.
∀ x7 .
x2
(
λ x9 .
x5
)
0
=
setsum
(
x0
(
λ x9 :
(
(
ι → ι
)
→ ι
)
→ ι
.
x6
0
)
(
Inj1
(
x4
0
)
)
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
λ x11 .
0
)
(
x3
(
λ x9 .
λ x10 :
ι →
(
ι → ι
)
→
ι → ι
.
0
)
(
x0
(
λ x9 :
(
(
ι → ι
)
→ ι
)
→ ι
.
x6
0
)
(
setsum
0
0
)
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
λ x11 .
x9
(
λ x12 .
0
)
)
0
)
(
Inj1
(
Inj0
0
)
)
(
λ x9 :
ι → ι
.
Inj0
(
Inj0
0
)
)
(
λ x9 .
0
)
(
setsum
x5
x5
)
)
)
(
setsum
(
x1
(
λ x9 .
setsum
(
x1
(
λ x10 .
0
)
0
)
0
)
(
Inj1
x7
)
)
(
x0
(
λ x9 :
(
(
ι → ι
)
→ ι
)
→ ι
.
0
)
x5
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
λ x11 .
setsum
x7
(
setsum
0
0
)
)
(
x2
(
λ x9 .
x2
(
λ x10 .
0
)
0
)
0
)
)
)
)
⟶
(
∀ x4 :
(
ι →
ι → ι
)
→ ι
.
∀ x5 .
∀ x6 :
(
ι →
ι → ι
)
→ ι
.
∀ x7 .
x2
(
λ x9 .
0
)
(
Inj0
0
)
=
x5
)
⟶
(
∀ x4 :
(
ι → ι
)
→
ι → ι
.
∀ x5 x6 .
∀ x7 :
(
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
x1
(
λ x9 .
Inj0
(
Inj1
0
)
)
(
x2
(
λ x9 .
x5
)
(
x0
(
λ x9 :
(
(
ι → ι
)
→ ι
)
→ ι
.
0
)
(
x2
(
λ x9 .
setsum
0
0
)
(
Inj0
0
)
)
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
λ x11 .
x7
(
λ x12 .
setsum
0
0
)
0
(
λ x12 .
x3
(
λ x13 .
λ x14 :
ι →
(
ι → ι
)
→
ι → ι
.
0
)
0
0
(
λ x13 :
ι → ι
.
0
)
(
λ x13 .
0
)
0
)
(
x1
(
λ x12 .
0
)
0
)
)
(
x2
(
λ x9 .
Inj0
0
)
0
)
)
)
=
x2
(
λ x9 .
x7
(
λ x10 .
x2
(
λ x11 .
x7
(
λ x12 .
x2
(
λ x13 .
0
)
0
)
(
x2
(
λ x12 .
0
)
0
)
(
λ x12 .
0
)
(
x0
(
λ x12 :
(
(
ι → ι
)
→ ι
)
→ ι
.
0
)
0
(
λ x12 :
(
ι → ι
)
→ ι
.
λ x13 :
ι → ι
.
λ x14 .
0
)
0
)
)
x9
)
(
x2
(
λ x10 .
setsum
(
setsum
0
0
)
(
x7
(
λ x11 .
0
)
0
(
λ x11 .
0
)
0
)
)
x6
)
(
λ x10 .
x10
)
(
Inj1
(
Inj1
0
)
)
)
x5
)
⟶
(
∀ x4 x5 :
ι → ι
.
∀ x6 :
(
ι → ι
)
→ ι
.
∀ x7 .
x1
(
λ x9 .
0
)
(
setsum
(
x4
0
)
x7
)
=
x6
(
λ x9 .
x6
(
λ x10 .
x10
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 x6 x7 .
x0
(
λ x9 :
(
(
ι → ι
)
→ ι
)
→ ι
.
0
)
x6
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
λ x11 .
setsum
(
x2
(
λ x12 .
Inj1
(
Inj0
0
)
)
x7
)
x7
)
0
=
x6
)
⟶
(
∀ x4 :
ι →
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
∀ x5 :
ι →
ι → ι
.
∀ x6 .
∀ x7 :
(
ι →
(
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
x0
(
λ x9 :
(
(
ι → ι
)
→ ι
)
→ ι
.
x2
(
λ x10 .
0
)
x6
)
(
Inj1
0
)
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
λ x11 .
setsum
(
x10
0
)
0
)
(
x3
(
λ x9 .
λ x10 :
ι →
(
ι → ι
)
→
ι → ι
.
x2
(
λ x11 .
setsum
(
x2
(
λ x12 .
0
)
0
)
(
x0
(
λ x12 :
(
(
ι → ι
)
→ ι
)
→ ι
.
0
)
0
(
λ x12 :
(
ι → ι
)
→ ι
.
λ x13 :
ι → ι
.
λ x14 .
0
)
0
)
)
(
x7
(
λ x11 .
λ x12 :
ι → ι
.
x12
0
)
(
λ x11 :
ι → ι
.
0
)
)
)
(
x5
(
Inj0
(
x5
0
0
)
)
0
)
(
x3
(
λ x9 .
λ x10 :
ι →
(
ι → ι
)
→
ι → ι
.
x6
)
(
Inj1
(
Inj1
0
)
)
(
x0
(
λ x9 :
(
(
ι → ι
)
→ ι
)
→ ι
.
x1
(
λ x10 .
0
)
0
)
x6
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
λ x11 .
0
)
(
x5
0
0
)
)
(
λ x9 :
ι → ι
.
x9
(
x1
(
λ x10 .
0
)
0
)
)
(
λ x9 .
x5
(
x7
(
λ x10 .
λ x11 :
ι → ι
.
0
)
(
λ x10 :
ι → ι
.
0
)
)
0
)
0
)
(
λ x9 :
ι → ι
.
x9
(
x0
(
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
Inj1
0
)
(
x9
0
)
(
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 :
ι → ι
.
λ x12 .
0
)
(
x3
(
λ x10 .
λ x11 :
ι →
(
ι → ι
)
→
ι → ι
.
0
)
0
0
(
λ x10 :
ι → ι
.
0
)
(
λ x10 .
0
)
0
)
)
)
(
λ x9 .
0
)
(
x4
(
Inj0
(
x0
(
λ x9 :
(
(
ι → ι
)
→ ι
)
→ ι
.
0
)
0
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
λ x11 .
0
)
0
)
)
(
λ x9 :
ι → ι
.
x2
(
λ x10 .
x3
(
λ x11 .
λ x12 :
ι →
(
ι → ι
)
→
ι → ι
.
0
)
0
0
(
λ x11 :
ι → ι
.
0
)
(
λ x11 .
0
)
0
)
x6
)
(
x2
(
λ x9 .
0
)
(
Inj0
0
)
)
(
Inj0
(
x1
(
λ x9 .
0
)
0
)
)
)
)
=
Inj0
0
)
⟶
False
(proof)
Theorem
7c1fe..
:
∀ x0 :
(
(
(
ι →
(
ι → ι
)
→
ι → ι
)
→
(
ι →
ι → ι
)
→
ι →
ι → ι
)
→
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ 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
.
∀ x2 :
(
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→
ι →
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
∀ x3 :
(
ι → ι
)
→
ι →
(
(
ι →
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
(
∀ x4 x5 x6 x7 .
x3
(
λ x9 .
0
)
0
(
λ x9 :
ι →
ι → ι
.
Inj0
(
Inj0
(
Inj1
0
)
)
)
(
λ x9 .
x9
)
=
x6
)
⟶
(
∀ x4 :
(
(
ι →
ι → ι
)
→ ι
)
→ ι
.
∀ x5 x6 .
∀ x7 :
ι → ι
.
x3
(
λ x9 .
Inj1
(
Inj0
0
)
)
(
x7
(
x1
(
λ x9 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 .
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 x13 .
Inj0
(
Inj1
0
)
)
(
λ x9 .
setsum
(
Inj1
0
)
(
setsum
0
0
)
)
(
λ x9 :
ι →
ι → ι
.
λ x10 x11 .
setsum
(
Inj0
0
)
0
)
(
λ x9 :
ι → ι
.
0
)
0
(
x4
(
λ x9 :
ι →
ι → ι
.
x7
0
)
)
)
)
(
λ x9 :
ι →
ι → ι
.
0
)
(
λ x9 .
0
)
=
Inj1
(
x7
(
Inj0
(
x0
(
λ x9 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
(
ι →
ι → ι
)
→
ι →
ι → ι
.
λ x10 x11 .
x9
(
λ x12 .
λ x13 :
ι → ι
.
λ x14 .
0
)
(
λ x12 x13 .
0
)
0
0
)
(
λ x9 .
0
)
)
)
)
)
⟶
(
∀ x4 :
ι →
(
ι → ι
)
→
ι → ι
.
∀ x5 x6 .
∀ x7 :
(
(
(
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
x2
(
λ x9 :
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
λ x10 .
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
x11
(
λ x14 .
0
)
(
x2
(
λ x14 :
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
λ x15 .
λ x16 :
(
ι → ι
)
→
ι → ι
.
λ x17 :
ι → ι
.
λ x18 .
0
)
(
x0
(
λ x14 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
(
ι →
ι → ι
)
→
ι →
ι → ι
.
λ x15 x16 .
x13
)
(
λ x14 .
x1
(
λ x15 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
λ x16 .
λ x17 :
(
ι → ι
)
→ ι
.
λ x18 x19 .
0
)
(
λ x15 .
0
)
(
λ x15 :
ι →
ι → ι
.
λ x16 x17 .
0
)
(
λ x15 :
ι → ι
.
0
)
0
0
)
)
)
)
(
setsum
0
(
x2
(
λ x9 :
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
λ x10 .
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
x13
)
(
Inj0
0
)
)
)
=
x5
)
⟶
(
∀ x4 :
ι →
ι → ι
.
∀ x5 :
(
ι →
ι → ι
)
→ ι
.
∀ x6 :
ι → ι
.
∀ x7 .
x2
(
λ x9 :
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
λ x10 .
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
x10
)
0
=
x6
0
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 :
(
(
ι →
ι → ι
)
→
ι → ι
)
→
ι → ι
.
∀ x7 .
x1
(
λ x9 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 .
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 x13 .
0
)
(
λ x9 .
0
)
(
λ x9 :
ι →
ι → ι
.
λ x10 x11 .
x10
)
(
λ x9 :
ι → ι
.
setsum
(
Inj1
(
x0
(
λ x10 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
(
ι →
ι → ι
)
→
ι →
ι → ι
.
λ x11 x12 .
Inj0
0
)
(
λ x10 .
x2
(
λ x11 :
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
λ x12 .
λ x13 :
(
ι → ι
)
→
ι → ι
.
λ x14 :
ι → ι
.
λ x15 .
0
)
0
)
)
)
(
setsum
(
x2
(
λ x10 :
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
λ x11 .
λ x12 :
(
ι → ι
)
→
ι → ι
.
λ x13 :
ι → ι
.
λ x14 .
x2
(
λ x15 :
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
λ x16 .
λ x17 :
(
ι → ι
)
→
ι → ι
.
λ x18 :
ι → ι
.
λ x19 .
0
)
0
)
(
setsum
0
0
)
)
(
x5
(
Inj1
0
)
)
)
)
0
(
Inj0
(
x2
(
λ x9 :
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
λ x10 .
λ x11 :
(
ι → ι
)
→
ι → ι
.
λ x12 :
ι → ι
.
x1
(
λ x13 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
λ x14 .
λ x15 :
(
ι → ι
)
→ ι
.
λ x16 x17 .
x14
)
(
λ x13 .
x13
)
(
λ x13 :
ι →
ι → ι
.
λ x14 x15 .
setsum
0
0
)
(
λ x13 :
ι → ι
.
0
)
(
x1
(
λ x13 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
λ x14 .
λ x15 :
(
ι → ι
)
→ ι
.
λ x16 x17 .
0
)
(
λ x13 .
0
)
(
λ x13 :
ι →
ι → ι
.
λ x14 x15 .
0
)
(
λ x13 :
ι → ι
.
0
)
0
0
)
)
x4
)
)
=
setsum
(
x1
(
λ x9 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 .
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 x13 .
0
)
(
λ x9 .
x2
(
λ x10 :
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
λ x11 .
λ x12 :
(
ι → ι
)
→
ι → ι
.
λ x13 :
ι → ι
.
λ x14 .
0
)
0
)
(
λ x9 :
ι →
ι → ι
.
λ x10 x11 .
0
)
(
λ x9 :
ι → ι
.
x0
(
λ x10 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
(
ι →
ι → ι
)
→
ι →
ι → ι
.
λ x11 x12 .
0
)
(
λ x10 .
x10
)
)
(
setsum
0
(
setsum
0
0
)
)
(
x0
(
λ x9 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
(
ι →
ι → ι
)
→
ι →
ι → ι
.
λ x10 x11 .
x0
(
λ x12 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
(
ι →
ι → ι
)
→
ι →
ι → ι
.
λ x13 x14 .
x13
)
(
λ x12 .
0
)
)
(
λ x9 .
x3
(
λ x10 .
x1
(
λ x11 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
λ x12 .
λ x13 :
(
ι → ι
)
→ ι
.
λ x14 x15 .
0
)
(
λ x11 .
0
)
(
λ x11 :
ι →
ι → ι
.
λ x12 x13 .
0
)
(
λ x11 :
ι → ι
.
0
)
0
0
)
x7
(
λ x10 :
ι →
ι → ι
.
setsum
0
0
)
(
λ x10 .
x2
(
λ x11 :
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
λ x12 .
λ x13 :
(
ι → ι
)
→
ι → ι
.
λ x14 :
ι → ι
.
λ x15 .
0
)
0
)
)
)
)
0
)
⟶
(
∀ x4 x5 :
(
(
ι →
ι → ι
)
→ ι
)
→ ι
.
∀ x6 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
∀ x7 :
ι → ι
.
x1
(
λ x9 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 .
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 x13 .
x0
(
λ x14 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
(
ι →
ι → ι
)
→
ι →
ι → ι
.
λ x15 x16 .
0
)
(
λ x14 .
0
)
)
(
setsum
(
setsum
(
Inj0
(
x6
(
λ x9 .
λ x10 :
ι → ι
.
0
)
)
)
(
Inj0
0
)
)
)
(
λ x9 :
ι →
ι → ι
.
λ x10 x11 .
setsum
(
x3
(
λ x12 .
setsum
0
0
)
(
x9
0
(
setsum
0
0
)
)
(
λ x12 :
ι →
ι → ι
.
0
)
(
λ x12 .
Inj1
(
x9
0
0
)
)
)
0
)
(
λ x9 :
ι → ι
.
x6
(
λ x10 .
λ x11 :
ι → ι
.
x7
(
x9
(
x3
(
λ x12 .
0
)
0
(
λ x12 :
ι →
ι → ι
.
0
)
(
λ x12 .
0
)
)
)
)
)
(
Inj1
0
)
(
x1
(
λ x9 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 .
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 x13 .
0
)
(
λ x9 .
0
)
(
λ x9 :
ι →
ι → ι
.
λ x10 x11 .
Inj1
(
x0
(
λ x12 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
(
ι →
ι → ι
)
→
ι →
ι → ι
.
λ x13 x14 .
x14
)
(
λ x12 .
x1
(
λ x13 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
λ x14 .
λ x15 :
(
ι → ι
)
→ ι
.
λ x16 x17 .
0
)
(
λ x13 .
0
)
(
λ x13 :
ι →
ι → ι
.
λ x14 x15 .
0
)
(
λ x13 :
ι → ι
.
0
)
0
0
)
)
)
(
λ x9 :
ι → ι
.
x2
(
λ x10 :
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
λ x11 .
λ x12 :
(
ι → ι
)
→
ι → ι
.
λ x13 :
ι → ι
.
λ x14 .
Inj0
(
setsum
0
0
)
)
(
Inj1
(
setsum
0
0
)
)
)
0
0
)
=
x1
(
λ x9 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 .
λ x11 :
(
ι → ι
)
→ ι
.
λ x12 x13 .
setsum
(
Inj1
(
x2
(
λ x14 :
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
λ x15 .
λ x16 :
(
ι → ι
)
→
ι → ι
.
λ x17 :
ι → ι
.
λ x18 .
x16
(
λ x19 .
0
)
0
)
0
)
)
x12
)
(
λ x9 .
Inj0
0
)
(
λ x9 :
ι →
ι → ι
.
λ x10 x11 .
x10
)
(
λ x9 :
ι → ι
.
x0
(
λ x10 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
(
ι →
ι → ι
)
→
ι →
ι → ι
.
λ x11 x12 .
0
)
(
λ x10 .
Inj0
(
Inj0
(
setsum
0
0
)
)
)
)
(
x0
(
λ x9 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
(
ι →
ι → ι
)
→
ι →
ι → ι
.
λ x10 x11 .
x10
)
(
λ x9 .
setsum
(
x6
(
λ x10 .
λ x11 :
ι → ι
.
Inj0
0
)
)
(
x2
(
λ x10 :
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
λ x11 .
λ x12 :
(
ι → ι
)
→
ι → ι
.
λ x13 :
ι → ι
.
λ x14 .
x14
)
(
setsum
0
0
)
)
)
)
(
setsum
(
x3
(
λ x9 .
Inj0
0
)
(
x3
(
λ x9 .
0
)
(
x0
(
λ x9 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
(
ι →
ι → ι
)
→
ι →
ι → ι
.
λ x10 x11 .
0
)
(
λ x9 .
0
)
)
(
λ x9 :
ι →
ι → ι
.
x5
(
λ x10 :
ι →
ι → ι
.
0
)
)
(
λ x9 .
0
)
)
(
λ x9 :
ι →
ι → ι
.
0
)
(
λ x9 .
x5
(
λ x10 :
ι →
ι → ι
.
x3
(
λ x11 .
0
)
0
(
λ x11 :
ι →
ι → ι
.
0
)
(
λ x11 .
0
)
)
)
)
(
x6
(
λ x9 .
λ x10 :
ι → ι
.
x10
x9
)
)
)
)
⟶
(
∀ x4 :
ι →
(
ι →
ι → ι
)
→
ι → ι
.
∀ x5 :
ι → ι
.
∀ x6 :
(
ι → ι
)
→
ι →
ι →
ι → ι
.
∀ x7 .
x0
(
λ x9 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
(
ι →
ι → ι
)
→
ι →
ι → ι
.
λ x10 x11 .
x10
)
(
λ x9 .
setsum
(
setsum
(
setsum
(
Inj1
0
)
0
)
(
x3
(
λ x10 .
0
)
x7
(
λ x10 :
ι →
ι → ι
.
setsum
0
0
)
(
λ x10 .
Inj0
0
)
)
)
(
x5
(
x1
(
λ x10 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 .
λ x12 :
(
ι → ι
)
→ ι
.
λ x13 x14 .
setsum
0
0
)
(
λ x10 .
Inj0
0
)
(
λ x10 :
ι →
ι → ι
.
λ x11 x12 .
setsum
0
0
)
(
λ x10 :
ι → ι
.
x0
(
λ x11 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
(
ι →
ι → ι
)
→
ι →
ι → ι
.
λ x12 x13 .
0
)
(
λ x11 .
0
)
)
0
0
)
)
)
=
setsum
(
Inj1
0
)
0
)
⟶
(
∀ x4 :
ι →
ι → ι
.
∀ x5 :
(
ι →
ι →
ι → ι
)
→ ι
.
∀ x6 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι →
ι →
ι → ι
.
∀ x7 .
x0
(
λ x9 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
(
ι →
ι → ι
)
→
ι →
ι → ι
.
λ x10 x11 .
setsum
x7
(
x2
(
λ x12 :
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
λ x13 .
λ x14 :
(
ι → ι
)
→
ι → ι
.
λ x15 :
ι → ι
.
λ x16 .
x0
(
λ x17 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
(
ι →
ι → ι
)
→
ι →
ι → ι
.
λ x18 x19 .
Inj1
0
)
(
λ x17 .
Inj1
0
)
)
(
Inj0
(
Inj1
0
)
)
)
)
(
λ x9 .
x3
(
λ x10 .
x0
(
λ x11 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
(
ι →
ι → ι
)
→
ι →
ι → ι
.
λ x12 x13 .
0
)
(
setsum
(
Inj0
0
)
)
)
(
Inj0
(
setsum
x7
(
x1
(
λ x10 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 .
λ x12 :
(
ι → ι
)
→ ι
.
λ x13 x14 .
0
)
(
λ x10 .
0
)
(
λ x10 :
ι →
ι → ι
.
λ x11 x12 .
0
)
(
λ x10 :
ι → ι
.
0
)
0
0
)
)
)
(
λ x10 :
ι →
ι → ι
.
x0
(
λ x11 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
(
ι →
ι → ι
)
→
ι →
ι → ι
.
λ x12 x13 .
x0
(
λ x14 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
(
ι →
ι → ι
)
→
ι →
ι → ι
.
λ x15 x16 .
x15
)
(
λ x14 .
0
)
)
(
λ x11 .
x11
)
)
(
λ x10 .
x9
)
)
=
x3
(
λ x9 .
x6
(
λ x10 .
λ x11 :
ι → ι
.
x9
)
x9
(
x6
(
λ x10 .
λ x11 :
ι → ι
.
0
)
(
x6
(
λ x10 .
λ x11 :
ι → ι
.
x11
0
)
(
Inj1
0
)
(
setsum
0
0
)
(
x0
(
λ x10 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
(
ι →
ι → ι
)
→
ι →
ι → ι
.
λ x11 x12 .
0
)
(
λ x10 .
0
)
)
)
(
x3
(
λ x10 .
0
)
x7
(
λ x10 :
ι →
ι → ι
.
setsum
0
0
)
(
λ x10 .
x1
(
λ x11 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
λ x12 .
λ x13 :
(
ι → ι
)
→ ι
.
λ x14 x15 .
0
)
(
λ x11 .
0
)
(
λ x11 :
ι →
ι → ι
.
λ x12 x13 .
0
)
(
λ x11 :
ι → ι
.
0
)
0
0
)
)
(
x6
(
λ x10 .
λ x11 :
ι → ι
.
setsum
0
0
)
0
(
Inj1
0
)
(
x1
(
λ x10 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 .
λ x12 :
(
ι → ι
)
→ ι
.
λ x13 x14 .
0
)
(
λ x10 .
0
)
(
λ x10 :
ι →
ι → ι
.
λ x11 x12 .
0
)
(
λ x10 :
ι → ι
.
0
)
0
0
)
)
)
0
)
(
x6
(
λ x9 .
λ x10 :
ι → ι
.
x2
(
λ x11 :
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
λ x12 .
λ x13 :
(
ι → ι
)
→
ι → ι
.
λ x14 :
ι → ι
.
λ x15 .
setsum
0
(
setsum
0
0
)
)
x9
)
(
x3
(
λ x9 .
x1
(
λ x10 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 .
λ x12 :
(
ι → ι
)
→ ι
.
λ x13 x14 .
0
)
(
λ x10 .
x9
)
(
λ x10 :
ι →
ι → ι
.
λ x11 x12 .
Inj0
0
)
(
λ x10 :
ι → ι
.
x9
)
(
x2
(
λ x10 :
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
λ x11 .
λ x12 :
(
ι → ι
)
→
ι → ι
.
λ x13 :
ι → ι
.
λ x14 .
0
)
0
)
0
)
(
x5
(
λ x9 x10 x11 .
setsum
0
0
)
)
(
λ x9 :
ι →
ι → ι
.
x9
(
Inj0
0
)
(
x6
(
λ x10 .
λ x11 :
ι → ι
.
0
)
0
0
0
)
)
(
λ x9 .
x6
(
λ x10 .
λ x11 :
ι → ι
.
x3
(
λ x12 .
0
)
0
(
λ x12 :
ι →
ι → ι
.
0
)
(
λ x12 .
0
)
)
0
x7
(
Inj1
0
)
)
)
(
x5
(
λ x9 x10 x11 .
Inj0
0
)
)
x7
)
(
λ x9 :
ι →
ι → ι
.
Inj0
(
x5
(
λ x10 x11 x12 .
setsum
(
Inj1
0
)
(
Inj0
0
)
)
)
)
(
λ x9 .
x3
(
λ x10 .
Inj0
x9
)
(
x2
(
λ x10 :
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
λ x11 .
λ x12 :
(
ι → ι
)
→
ι → ι
.
λ x13 :
ι → ι
.
λ x14 .
0
)
(
x5
(
λ x10 x11 x12 .
x12
)
)
)
(
λ x10 :
ι →
ι → ι
.
Inj1
(
x10
0
(
Inj1
0
)
)
)
(
λ x10 .
0
)
)
)
⟶
False
(proof)
Theorem
92643..
:
∀ x0 :
(
ι →
ι → ι
)
→
ι → ι
.
∀ x1 :
(
ι → ι
)
→
ι →
ι →
(
ι → ι
)
→
ι → ι
.
∀ x2 :
(
(
ι →
(
ι →
ι → ι
)
→ ι
)
→
ι → ι
)
→
ι → ι
.
∀ x3 :
(
ι → ι
)
→
ι → ι
.
(
∀ x4 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
∀ x5 x6 .
∀ x7 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
x3
(
λ x9 .
x3
(
λ x10 .
x2
(
λ x11 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x12 .
x0
(
λ x13 x14 .
x11
0
(
λ x15 x16 .
0
)
)
(
setsum
0
0
)
)
(
x3
(
λ x11 .
x11
)
x6
)
)
(
x1
(
λ x10 .
x7
(
λ x11 :
(
ι → ι
)
→ ι
.
0
)
(
λ x11 :
ι → ι
.
Inj0
0
)
(
setsum
0
0
)
)
0
(
x0
(
λ x10 x11 .
x9
)
x9
)
(
λ x10 .
Inj0
0
)
(
Inj0
(
setsum
0
0
)
)
)
)
(
x2
(
λ x9 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x10 .
setsum
(
x9
(
Inj0
0
)
(
λ x11 x12 .
0
)
)
(
setsum
(
x1
(
λ x11 .
0
)
0
0
(
λ x11 .
0
)
0
)
(
setsum
0
0
)
)
)
x5
)
=
x2
(
λ x9 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x10 .
Inj0
0
)
(
x4
(
λ x9 :
ι →
ι → ι
.
λ x10 :
ι → ι
.
λ x11 .
setsum
(
Inj0
0
)
0
)
(
x7
(
λ x9 :
(
ι → ι
)
→ ι
.
0
)
(
λ x9 :
ι → ι
.
x7
(
λ x10 :
(
ι → ι
)
→ ι
.
x2
(
λ x11 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x12 .
0
)
0
)
(
λ x10 :
ι → ι
.
x1
(
λ x11 .
0
)
0
0
(
λ x11 .
0
)
0
)
0
)
(
Inj1
x6
)
)
(
λ x9 .
x2
(
λ x10 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x11 .
setsum
(
Inj0
0
)
(
x10
0
(
λ x12 x13 .
0
)
)
)
(
Inj0
(
setsum
0
0
)
)
)
(
setsum
x5
(
x1
(
λ x9 .
x3
(
λ x10 .
0
)
0
)
(
setsum
0
0
)
(
setsum
0
0
)
(
λ x9 .
0
)
(
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
(
ι → ι
)
→ ι
.
∀ x7 .
x3
(
λ x9 .
Inj1
0
)
(
x0
(
λ x9 x10 .
x3
(
λ x11 .
setsum
0
(
x1
(
λ x12 .
0
)
0
0
(
λ x12 .
0
)
0
)
)
(
x3
(
λ x11 .
x0
(
λ x12 x13 .
0
)
0
)
0
)
)
x4
)
=
Inj1
x7
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 x6 .
∀ x7 :
ι →
(
ι →
ι → ι
)
→ ι
.
x2
(
λ x9 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x10 .
Inj0
(
x1
(
λ x11 .
x9
(
x9
0
(
λ x12 x13 .
0
)
)
(
λ x12 x13 .
setsum
0
0
)
)
(
Inj1
(
setsum
0
0
)
)
(
x3
(
λ x11 .
Inj1
0
)
(
setsum
0
0
)
)
(
λ x11 .
x11
)
0
)
)
0
=
Inj1
(
x4
(
x3
(
λ x9 .
0
)
(
Inj0
(
setsum
0
0
)
)
)
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
ι → ι
.
∀ x7 .
x2
(
λ x9 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x10 .
setsum
(
Inj0
(
Inj0
(
x9
0
(
λ x11 x12 .
0
)
)
)
)
(
x3
(
λ x11 .
setsum
(
Inj0
0
)
(
x3
(
λ x12 .
0
)
0
)
)
x7
)
)
(
x0
(
λ x9 x10 .
0
)
(
setsum
x4
(
Inj1
(
x1
(
λ x9 .
0
)
0
0
(
λ x9 .
0
)
0
)
)
)
)
=
x0
(
λ x9 x10 .
Inj1
x7
)
(
setsum
(
setsum
(
x6
0
)
(
x1
(
λ x9 .
setsum
0
0
)
(
setsum
0
0
)
(
Inj0
0
)
(
λ x9 .
x2
(
λ x10 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x11 .
0
)
0
)
(
setsum
0
0
)
)
)
x4
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x7 .
x1
(
λ x9 .
0
)
0
0
(
λ x9 .
x6
x5
(
λ x10 x11 .
0
)
(
λ x10 .
x9
)
)
(
x0
(
λ x9 x10 .
Inj1
(
Inj1
(
setsum
0
0
)
)
)
(
setsum
(
Inj1
0
)
(
x1
(
λ x9 .
x1
(
λ x10 .
0
)
0
0
(
λ x10 .
0
)
0
)
0
0
(
λ x9 .
0
)
(
x0
(
λ x9 x10 .
0
)
0
)
)
)
)
=
x0
(
λ x9 x10 .
x2
(
λ x11 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x12 .
0
)
(
setsum
x10
(
x3
(
λ x11 .
0
)
(
x2
(
λ x11 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x12 .
0
)
0
)
)
)
)
(
Inj0
(
Inj1
x4
)
)
)
⟶
(
∀ x4 .
∀ x5 :
(
ι → ι
)
→ ι
.
∀ x6 x7 .
x1
(
λ x9 .
Inj1
0
)
(
x3
(
λ x9 .
x2
(
λ x10 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x11 .
x7
)
0
)
0
)
0
(
λ x9 .
x6
)
(
Inj1
(
setsum
(
Inj1
(
setsum
0
0
)
)
0
)
)
=
Inj1
(
x3
(
λ x9 .
0
)
(
Inj1
0
)
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→
ι →
ι → ι
.
∀ x5 .
∀ x6 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι →
ι → ι
.
∀ x7 .
x0
(
λ x9 x10 .
x1
(
λ x11 .
x1
(
λ x12 .
x11
)
(
x3
(
λ x12 .
Inj0
0
)
(
x1
(
λ x12 .
0
)
0
0
(
λ x12 .
0
)
0
)
)
(
x0
(
λ x12 x13 .
x2
(
λ x14 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x15 .
0
)
0
)
x7
)
(
λ x12 .
x3
(
λ x13 .
x12
)
(
Inj1
0
)
)
x7
)
(
x0
(
λ x11 x12 .
setsum
(
x0
(
λ x13 x14 .
0
)
0
)
x11
)
0
)
x7
(
x2
(
λ x11 :
ι →
(
ι →
ι → ι
)
→ ι
.
λ x12 .
x1
(
λ x13 .
x3
(
λ x14 .
0
)
0
)
0
(
x11
0
(
λ x13 x14 .
0
)
)
(
λ x13 .
setsum
0
0
)
0
)
)
0
)
(
Inj0
(
Inj0
(
x3
(
λ x9 .
0
)
(
x6
(
λ x9 :
(
ι → ι
)
→ ι
.
0
)
0
0
)
)
)
)
=
Inj0
x7
)
⟶
(
∀ x4 .
∀ x5 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
∀ x6 :
(
ι → ι
)
→ ι
.
∀ x7 .
x0
(
λ x9 x10 .
setsum
0
0
)
(
setsum
0
0
)
=
x7
)
⟶
False
(proof)
Theorem
cbf3a..
:
∀ x0 :
(
ι →
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
(
ι →
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
.
∀ x1 :
(
ι →
(
ι → ι
)
→
(
ι →
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x2 :
(
ι →
ι →
ι →
(
ι → ι
)
→
ι → ι
)
→
ι →
ι →
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x3 :
(
ι → ι
)
→
ι → ι
.
(
∀ x4 :
ι →
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x5 :
ι →
(
ι → ι
)
→ ι
.
∀ x6 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x7 :
ι →
(
ι →
ι → ι
)
→ ι
.
x3
(
λ x9 .
0
)
(
setsum
0
(
x0
(
λ x9 .
λ x10 :
ι →
(
ι → ι
)
→
ι → ι
.
x2
(
λ x11 x12 x13 .
λ x14 :
ι → ι
.
λ x15 .
x3
(
λ x16 .
0
)
0
)
0
(
x7
0
(
λ x11 x12 .
0
)
)
(
λ x11 :
ι → ι
.
λ x12 .
x10
0
(
λ x13 .
0
)
0
)
(
λ x11 .
setsum
0
0
)
0
)
(
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x10 :
(
ι → ι
)
→ ι
.
setsum
(
x9
0
(
λ x11 .
0
)
0
)
0
)
)
)
=
x6
(
λ x9 :
(
ι → ι
)
→ ι
.
x1
(
λ x10 .
λ x11 :
ι → ι
.
λ x12 :
ι →
ι → ι
.
λ x13 .
0
)
(
λ x10 .
x0
(
λ x11 .
λ x12 :
ι →
(
ι → ι
)
→
ι → ι
.
x11
)
(
λ x11 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x12 :
(
ι → ι
)
→ ι
.
x10
)
)
)
(
λ x9 .
setsum
(
x5
(
x0
(
λ x10 .
λ x11 :
ι →
(
ι → ι
)
→
ι → ι
.
x11
0
(
λ x12 .
0
)
0
)
(
λ x10 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x11 :
(
ι → ι
)
→ ι
.
setsum
0
0
)
)
(
λ x10 .
x9
)
)
(
x6
(
λ x10 :
(
ι → ι
)
→ ι
.
x9
)
(
λ x10 .
x10
)
(
λ x10 .
0
)
(
x2
(
λ x10 x11 x12 .
λ x13 :
ι → ι
.
λ x14 .
x3
(
λ x15 .
0
)
0
)
(
setsum
0
0
)
(
Inj0
0
)
(
λ x10 :
ι → ι
.
λ x11 .
0
)
(
λ x10 .
Inj1
0
)
x9
)
)
)
Inj1
(
Inj1
(
x0
(
λ x9 .
λ x10 :
ι →
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x10 :
(
ι → ι
)
→ ι
.
0
)
)
)
)
⟶
(
∀ x4 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x5 :
ι →
ι →
ι → ι
.
∀ x6 :
(
ι → ι
)
→ ι
.
∀ x7 .
x3
(
λ x9 .
0
)
(
x6
(
λ x9 .
x6
(
λ x10 .
0
)
)
)
=
setsum
(
x0
(
λ x9 .
λ x10 :
ι →
(
ι → ι
)
→
ι → ι
.
Inj1
(
x2
(
λ x11 x12 x13 .
λ x14 :
ι → ι
.
λ x15 .
x1
(
λ x16 .
λ x17 :
ι → ι
.
λ x18 :
ι →
ι → ι
.
λ x19 .
0
)
(
λ x16 .
0
)
)
0
(
x2
(
λ x11 x12 x13 .
λ x14 :
ι → ι
.
λ x15 .
0
)
0
0
(
λ x11 :
ι → ι
.
λ x12 .
0
)
(
λ x11 .
0
)
0
)
(
λ x11 :
ι → ι
.
λ x12 .
x12
)
(
λ x11 .
x11
)
0
)
)
(
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x10 :
(
ι → ι
)
→ ι
.
setsum
(
setsum
(
setsum
0
0
)
0
)
(
x2
(
λ x11 x12 x13 .
λ x14 :
ι → ι
.
λ x15 .
x0
(
λ x16 .
λ x17 :
ι →
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x16 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x17 :
(
ι → ι
)
→ ι
.
0
)
)
(
x10
(
λ x11 .
0
)
)
(
setsum
0
0
)
(
λ x11 :
ι → ι
.
λ x12 .
x12
)
(
λ x11 .
Inj0
0
)
(
x6
(
λ x11 .
0
)
)
)
)
)
(
x2
(
λ x9 x10 x11 .
λ x12 :
ι → ι
.
λ x13 .
0
)
(
x1
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 :
ι →
ι → ι
.
λ x12 .
0
)
(
λ x9 .
x6
(
λ x10 .
x6
(
λ x11 .
0
)
)
)
)
(
x2
(
λ x9 x10 x11 .
λ x12 :
ι → ι
.
λ x13 .
0
)
(
x5
0
(
x1
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 :
ι →
ι → ι
.
λ x12 .
0
)
(
λ x9 .
0
)
)
(
x4
0
(
λ x9 :
ι → ι
.
λ x10 .
0
)
(
λ x9 .
0
)
)
)
(
x3
(
λ x9 .
0
)
0
)
(
λ x9 :
ι → ι
.
λ x10 .
x0
(
λ x11 .
λ x12 :
ι →
(
ι → ι
)
→
ι → ι
.
setsum
0
0
)
(
λ x11 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x12 :
(
ι → ι
)
→ ι
.
0
)
)
(
λ x9 .
Inj0
0
)
(
x2
(
λ x9 x10 x11 .
λ x12 :
ι → ι
.
λ x13 .
x0
(
λ x14 .
λ x15 :
ι →
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x14 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x15 :
(
ι → ι
)
→ ι
.
0
)
)
(
x2
(
λ x9 x10 x11 .
λ x12 :
ι → ι
.
λ x13 .
0
)
0
0
(
λ x9 :
ι → ι
.
λ x10 .
0
)
(
λ x9 .
0
)
0
)
0
(
λ x9 :
ι → ι
.
λ x10 .
x2
(
λ x11 x12 x13 .
λ x14 :
ι → ι
.
λ x15 .
0
)
0
0
(
λ x11 :
ι → ι
.
λ x12 .
0
)
(
λ x11 .
0
)
0
)
(
λ x9 .
x2
(
λ x10 x11 x12 .
λ x13 :
ι → ι
.
λ x14 .
0
)
0
0
(
λ x10 :
ι → ι
.
λ x11 .
0
)
(
λ x10 .
0
)
0
)
(
x4
0
(
λ x9 :
ι → ι
.
λ x10 .
0
)
(
λ x9 .
0
)
)
)
)
(
λ x9 :
ι → ι
.
x9
)
(
λ x9 .
x1
(
λ x10 .
λ x11 :
ι → ι
.
λ x12 :
ι →
ι → ι
.
λ x13 .
x12
0
(
x11
0
)
)
(
λ x10 .
x3
(
λ x11 .
0
)
x9
)
)
0
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
(
ι →
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
∀ x7 .
x2
(
λ x9 x10 x11 .
λ x12 :
ι → ι
.
λ x13 .
x1
(
λ x14 .
λ x15 :
ι → ι
.
λ x16 :
ι →
ι → ι
.
λ x17 .
0
)
(
λ x14 .
x12
(
x12
0
)
)
)
(
x0
(
λ x9 .
λ x10 :
ι →
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x10 :
(
ι → ι
)
→ ι
.
x1
(
λ x11 .
λ x12 :
ι → ι
.
λ x13 :
ι →
ι → ι
.
λ x14 .
x3
(
λ x15 .
Inj1
0
)
(
x13
0
0
)
)
(
λ x11 .
x7
)
)
)
0
(
λ x9 :
ι → ι
.
λ x10 .
0
)
(
λ x9 .
0
)
(
x1
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 :
ι →
ι → ι
.
λ x12 .
0
)
(
λ x9 .
0
)
)
=
x0
(
λ x9 .
λ x10 :
ι →
(
ι → ι
)
→
ι → ι
.
x1
(
λ x11 .
λ x12 :
ι → ι
.
λ x13 :
ι →
ι → ι
.
λ x14 .
x1
(
λ x15 .
λ x16 :
ι → ι
.
λ x17 :
ι →
ι → ι
.
λ x18 .
x18
)
(
λ x15 .
0
)
)
(
λ x11 .
x11
)
)
(
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x10 :
(
ι → ι
)
→ ι
.
Inj1
(
x9
(
Inj0
(
x10
(
λ x11 .
0
)
)
)
(
λ x11 .
setsum
0
0
)
(
setsum
(
x0
(
λ x11 .
λ x12 :
ι →
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x11 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x12 :
(
ι → ι
)
→ ι
.
0
)
)
x7
)
)
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
∀ x5 :
ι → ι
.
∀ x6 x7 .
x2
(
λ x9 x10 x11 .
λ x12 :
ι → ι
.
λ x13 .
setsum
(
x3
(
λ x14 .
Inj0
x11
)
0
)
(
Inj1
(
Inj1
x13
)
)
)
(
x4
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
0
)
)
(
x1
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 :
ι →
ι → ι
.
λ x12 .
x11
0
(
x2
(
λ x13 x14 x15 .
λ x16 :
ι → ι
.
λ x17 .
x3
(
λ x18 .
0
)
0
)
0
(
x11
0
0
)
(
λ x13 :
ι → ι
.
λ x14 .
Inj0
0
)
(
λ x13 .
setsum
0
0
)
0
)
)
(
λ x9 .
x6
)
)
(
λ x9 :
ι → ι
.
λ x10 .
x10
)
(
λ x9 .
0
)
(
Inj1
(
Inj0
x7
)
)
=
x4
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
Inj0
(
x5
(
x2
(
λ x10 x11 x12 .
λ x13 :
ι → ι
.
λ x14 .
0
)
0
(
setsum
0
0
)
(
λ x10 :
ι → ι
.
λ x11 .
x1
(
λ x12 .
λ x13 :
ι → ι
.
λ x14 :
ι →
ι → ι
.
λ x15 .
0
)
(
λ x12 .
0
)
)
(
λ x10 .
x1
(
λ x11 .
λ x12 :
ι → ι
.
λ x13 :
ι →
ι → ι
.
λ x14 .
0
)
(
λ x11 .
0
)
)
0
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 .
∀ x7 :
ι → ι
.
x1
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 :
ι →
ι → ι
.
λ x12 .
x2
(
λ x13 x14 x15 .
λ x16 :
ι → ι
.
λ x17 .
x1
(
λ x18 .
λ x19 :
ι → ι
.
λ x20 :
ι →
ι → ι
.
λ x21 .
x19
0
)
(
λ x18 .
0
)
)
(
x10
(
x1
(
λ x13 .
λ x14 :
ι → ι
.
λ x15 :
ι →
ι → ι
.
λ x16 .
0
)
(
λ x13 .
0
)
)
)
(
Inj0
0
)
(
λ x13 :
ι → ι
.
λ x14 .
0
)
(
λ x13 .
x2
(
λ x14 x15 x16 .
λ x17 :
ι → ι
.
λ x18 .
0
)
0
0
(
λ x14 :
ι → ι
.
λ x15 .
x12
)
(
λ x14 .
Inj1
0
)
(
Inj0
0
)
)
0
)
(
λ x9 .
setsum
(
x7
(
x2
(
λ x10 x11 x12 .
λ x13 :
ι → ι
.
λ x14 .
Inj1
0
)
(
x1
(
λ x10 .
λ x11 :
ι → ι
.
λ x12 :
ι →
ι → ι
.
λ x13 .
0
)
(
λ x10 .
0
)
)
x9
(
λ x10 :
ι → ι
.
λ x11 .
setsum
0
0
)
(
λ x10 .
Inj0
0
)
0
)
)
(
x1
(
λ x10 .
λ x11 :
ι → ι
.
λ x12 :
ι →
ι → ι
.
λ x13 .
setsum
(
setsum
0
0
)
0
)
(
λ x10 .
x2
(
λ x11 x12 x13 .
λ x14 :
ι → ι
.
λ x15 .
x15
)
0
(
Inj1
0
)
(
λ x11 :
ι → ι
.
λ x12 .
x9
)
(
λ x11 .
x0
(
λ x12 .
λ x13 :
ι →
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x12 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x13 :
(
ι → ι
)
→ ι
.
0
)
)
x9
)
)
)
=
x2
(
λ x9 x10 x11 .
λ x12 :
ι → ι
.
λ x13 .
x1
(
λ x14 .
λ x15 :
ι → ι
.
λ x16 :
ι →
ι → ι
.
λ x17 .
0
)
(
λ x14 .
x13
)
)
(
Inj0
(
setsum
0
(
setsum
(
x1
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 :
ι →
ι → ι
.
λ x12 .
0
)
(
λ x9 .
0
)
)
0
)
)
)
(
setsum
(
x5
(
Inj1
x4
)
)
(
Inj0
(
x3
(
λ x9 .
x7
0
)
(
setsum
0
0
)
)
)
)
(
λ x9 :
ι → ι
.
λ x10 .
x9
(
x1
(
λ x11 .
λ x12 :
ι → ι
.
λ x13 :
ι →
ι → ι
.
λ x14 .
0
)
(
λ x11 .
x9
(
x9
0
)
)
)
)
(
λ x9 .
Inj0
(
x0
(
λ x10 .
λ x11 :
ι →
(
ι → ι
)
→
ι → ι
.
x3
(
λ x12 .
x1
(
λ x13 .
λ x14 :
ι → ι
.
λ x15 :
ι →
ι → ι
.
λ x16 .
0
)
(
λ x13 .
0
)
)
(
x0
(
λ x12 .
λ x13 :
ι →
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x12 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x13 :
(
ι → ι
)
→ ι
.
0
)
)
)
(
λ x10 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x11 :
(
ι → ι
)
→ ι
.
x2
(
λ x12 x13 x14 .
λ x15 :
ι → ι
.
λ x16 .
0
)
(
Inj0
0
)
x9
(
λ x12 :
ι → ι
.
λ x13 .
x13
)
(
λ x12 .
x12
)
(
setsum
0
0
)
)
)
)
(
x3
(
λ x9 .
x7
0
)
(
x7
x4
)
)
)
⟶
(
∀ x4 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
∀ x5 x6 :
ι →
ι →
(
ι → ι
)
→ ι
.
∀ x7 :
(
ι → ι
)
→
ι → ι
.
x1
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 :
ι →
ι → ι
.
λ x12 .
0
)
(
λ x9 .
setsum
(
setsum
(
x2
(
λ x10 x11 x12 .
λ x13 :
ι → ι
.
λ x14 .
x1
(
λ x15 .
λ x16 :
ι → ι
.
λ x17 :
ι →
ι → ι
.
λ x18 .
0
)
(
λ x15 .
0
)
)
(
x6
0
0
(
λ x10 .
0
)
)
(
Inj1
0
)
(
λ x10 :
ι → ι
.
λ x11 .
x9
)
(
λ x10 .
x1
(
λ x11 .
λ x12 :
ι → ι
.
λ x13 :
ι →
ι → ι
.
λ x14 .
0
)
(
λ x11 .
0
)
)
0
)
(
setsum
(
Inj1
0
)
(
x3
(
λ x10 .
0
)
0
)
)
)
(
x1
(
λ x10 .
λ x11 :
ι → ι
.
λ x12 :
ι →
ι → ι
.
λ x13 .
x12
(
x0
(
λ x14 .
λ x15 :
ι →
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x14 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x15 :
(
ι → ι
)
→ ι
.
0
)
)
(
x1
(
λ x14 .
λ x15 :
ι → ι
.
λ x16 :
ι →
ι → ι
.
λ x17 .
0
)
(
λ x14 .
0
)
)
)
(
λ x10 .
0
)
)
)
=
setsum
(
setsum
0
(
Inj1
(
Inj1
(
x0
(
λ x9 .
λ x10 :
ι →
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x10 :
(
ι → ι
)
→ ι
.
0
)
)
)
)
)
0
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 .
∀ x6 :
ι → ι
.
∀ x7 .
x0
(
λ x9 .
λ x10 :
ι →
(
ι → ι
)
→
ι → ι
.
setsum
(
Inj0
(
x10
(
setsum
0
0
)
(
λ x11 .
x1
(
λ x12 .
λ x13 :
ι → ι
.
λ x14 :
ι →
ι → ι
.
λ x15 .
0
)
(
λ x12 .
0
)
)
0
)
)
(
x3
(
λ x11 .
x0
(
λ x12 .
λ x13 :
ι →
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x12 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x13 :
(
ι → ι
)
→ ι
.
x2
(
λ x14 x15 x16 .
λ x17 :
ι → ι
.
λ x18 .
0
)
0
0
(
λ x14 :
ι → ι
.
λ x15 .
0
)
(
λ x14 .
0
)
0
)
)
(
x10
(
Inj0
0
)
(
λ x11 .
0
)
(
setsum
0
0
)
)
)
)
(
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x10 :
(
ι → ι
)
→ ι
.
Inj0
(
x3
(
λ x11 .
x7
)
0
)
)
=
x6
(
x1
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 :
ι →
ι → ι
.
λ x12 .
0
)
(
λ x9 .
x1
(
λ x10 .
λ x11 :
ι → ι
.
λ x12 :
ι →
ι → ι
.
λ x13 .
0
)
(
λ x10 .
Inj0
0
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
∀ x6 :
(
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x7 .
x0
(
λ x9 .
λ x10 :
ι →
(
ι → ι
)
→
ι → ι
.
x2
(
λ x11 x12 x13 .
λ x14 :
ι → ι
.
λ x15 .
Inj1
(
setsum
(
setsum
0
0
)
x13
)
)
0
(
setsum
0
(
x2
(
λ x11 x12 x13 .
λ x14 :
ι → ι
.
λ x15 .
setsum
0
0
)
0
(
setsum
0
0
)
(
λ x11 :
ι → ι
.
λ x12 .
0
)
(
λ x11 .
x9
)
(
x10
0
(
λ x11 .
0
)
0
)
)
)
(
λ x11 :
ι → ι
.
λ x12 .
0
)
(
λ x11 .
x10
x11
(
λ x12 .
x2
(
λ x13 x14 x15 .
λ x16 :
ι → ι
.
λ x17 .
x16
0
)
0
x12
(
λ x13 :
ι → ι
.
λ x14 .
x1
(
λ x15 .
λ x16 :
ι → ι
.
λ x17 :
ι →
ι → ι
.
λ x18 .
0
)
(
λ x15 .
0
)
)
(
λ x13 .
Inj1
0
)
0
)
x11
)
0
)
(
λ x9 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x10 :
(
ι → ι
)
→ ι
.
x7
)
=
setsum
(
setsum
0
x4
)
(
x5
(
λ x9 :
ι →
ι → ι
.
λ x10 :
ι → ι
.
λ x11 .
x0
(
λ x12 .
λ x13 :
ι →
(
ι → ι
)
→
ι → ι
.
setsum
(
Inj1
0
)
(
x13
0
(
λ x14 .
0
)
0
)
)
(
λ x12 :
ι →
(
ι → ι
)
→
ι → ι
.
λ x13 :
(
ι → ι
)
→ ι
.
0
)
)
0
)
)
⟶
False
(proof)
Theorem
66876..
:
∀ x0 :
(
ι →
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι →
ι →
ι → ι
)
→
(
ι → ι
)
→
ι →
ι →
(
ι → ι
)
→ ι
.
∀ x1 :
(
ι → ι
)
→
(
(
ι →
ι →
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→ ι
.
∀ x2 :
(
(
ι → ι
)
→ ι
)
→
(
(
(
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
.
∀ x3 :
(
(
ι → ι
)
→ ι
)
→
ι →
(
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
(
∀ x4 .
∀ x5 :
(
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x6 :
ι → ι
.
∀ x7 .
x3
(
λ x9 :
ι → ι
.
0
)
x7
(
λ x9 :
ι →
ι → ι
.
λ x10 :
ι → ι
.
λ x11 .
0
)
(
x0
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x11 x12 x13 .
x1
(
λ x14 .
0
)
(
λ x14 :
ι →
ι →
ι → ι
.
x1
(
λ x15 .
0
)
(
λ x15 :
ι →
ι →
ι → ι
.
Inj1
0
)
x13
(
λ x15 .
x1
(
λ x16 .
0
)
(
λ x16 :
ι →
ι →
ι → ι
.
0
)
0
(
λ x16 .
0
)
)
)
x11
(
λ x14 .
x0
(
λ x15 .
λ x16 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x17 x18 x19 .
x3
(
λ x20 :
ι → ι
.
0
)
0
(
λ x20 :
ι →
ι → ι
.
λ x21 :
ι → ι
.
λ x22 .
0
)
0
0
)
(
λ x15 .
x14
)
(
x0
(
λ x15 .
λ x16 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x17 x18 x19 .
0
)
(
λ x15 .
0
)
0
0
(
λ x15 .
0
)
)
(
setsum
0
0
)
(
λ x15 .
setsum
0
0
)
)
)
(
λ x9 .
x3
(
λ x10 :
ι → ι
.
x3
(
λ x11 :
ι → ι
.
x2
(
λ x12 :
ι → ι
.
0
)
(
λ x12 x13 :
(
ι → ι
)
→ ι
.
0
)
)
(
x1
(
λ x11 .
0
)
(
λ x11 :
ι →
ι →
ι → ι
.
0
)
0
(
λ x11 .
0
)
)
(
λ x11 :
ι →
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
0
)
(
Inj1
0
)
(
x6
0
)
)
0
(
λ x10 :
ι →
ι → ι
.
λ x11 :
ι → ι
.
λ x12 .
x3
(
λ x13 :
ι → ι
.
0
)
(
Inj0
0
)
(
λ x13 :
ι →
ι → ι
.
λ x14 :
ι → ι
.
λ x15 .
setsum
0
0
)
(
x1
(
λ x13 .
0
)
(
λ x13 :
ι →
ι →
ι → ι
.
0
)
0
(
λ x13 .
0
)
)
(
Inj1
0
)
)
0
x7
)
(
x5
(
λ x9 x10 :
ι → ι
.
λ x11 .
x10
(
x10
0
)
)
)
x4
(
λ x9 .
x7
)
)
(
x6
0
)
=
x0
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x11 x12 .
setsum
0
)
(
λ x9 .
x1
(
λ x10 .
0
)
(
λ x10 :
ι →
ι →
ι → ι
.
0
)
(
x1
(
λ x10 .
0
)
(
λ x10 :
ι →
ι →
ι → ι
.
x1
(
λ x11 .
x10
0
0
0
)
(
λ x11 :
ι →
ι →
ι → ι
.
0
)
(
x2
(
λ x11 :
ι → ι
.
0
)
(
λ x11 x12 :
(
ι → ι
)
→ ι
.
0
)
)
(
λ x11 .
x1
(
λ x12 .
0
)
(
λ x12 :
ι →
ι →
ι → ι
.
0
)
0
(
λ x12 .
0
)
)
)
(
x1
(
λ x10 .
setsum
0
0
)
(
λ x10 :
ι →
ι →
ι → ι
.
x0
(
λ x11 .
λ x12 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x13 x14 x15 .
0
)
(
λ x11 .
0
)
0
0
(
λ x11 .
0
)
)
0
(
λ x10 .
0
)
)
(
λ x10 .
x9
)
)
(
λ x10 .
x7
)
)
(
Inj0
(
x2
(
λ x9 :
ι → ι
.
x6
(
x0
(
λ x10 .
λ x11 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x12 x13 x14 .
0
)
(
λ x10 .
0
)
0
0
(
λ x10 .
0
)
)
)
(
λ x9 x10 :
(
ι → ι
)
→ ι
.
setsum
x7
0
)
)
)
(
setsum
(
setsum
0
0
)
x7
)
(
λ x9 .
setsum
0
(
setsum
0
(
setsum
(
x1
(
λ x10 .
0
)
(
λ x10 :
ι →
ι →
ι → ι
.
0
)
0
(
λ x10 .
0
)
)
x7
)
)
)
)
⟶
(
∀ x4 :
(
ι →
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x5 .
∀ x6 :
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x7 .
x3
(
λ x9 :
ι → ι
.
x9
(
setsum
x5
0
)
)
(
x4
(
λ x9 x10 x11 .
0
)
(
λ x9 .
setsum
x7
0
)
)
(
λ x9 :
ι →
ι → ι
.
λ x10 :
ι → ι
.
λ x11 .
x0
(
λ x12 .
λ x13 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x14 x15 x16 .
setsum
0
(
setsum
(
setsum
0
0
)
0
)
)
(
λ x12 .
Inj0
(
setsum
0
(
setsum
0
0
)
)
)
(
x0
(
λ x12 .
λ x13 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x14 x15 x16 .
x13
(
λ x17 :
ι → ι
.
setsum
0
0
)
(
λ x17 .
x14
)
0
)
(
λ x12 .
x11
)
(
setsum
x11
(
x9
0
0
)
)
(
setsum
x7
0
)
(
λ x12 .
0
)
)
(
x2
(
λ x12 :
ι → ι
.
x11
)
(
λ x12 x13 :
(
ι → ι
)
→ ι
.
0
)
)
(
λ x12 .
x10
0
)
)
(
x6
0
(
λ x9 x10 .
x7
)
(
λ x9 .
0
)
(
x4
(
λ x9 x10 x11 .
x10
)
(
λ x9 .
x7
)
)
)
(
x3
(
λ x9 :
ι → ι
.
x0
(
λ x10 .
λ x11 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x12 x13 x14 .
0
)
(
λ x10 .
x7
)
(
x6
0
(
λ x10 x11 .
Inj1
0
)
(
λ x10 .
x6
0
(
λ x11 x12 .
0
)
(
λ x11 .
0
)
0
)
(
x0
(
λ x10 .
λ x11 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x12 x13 x14 .
0
)
(
λ x10 .
0
)
0
0
(
λ x10 .
0
)
)
)
(
x2
(
λ x10 :
ι → ι
.
Inj1
0
)
(
λ x10 x11 :
(
ι → ι
)
→ ι
.
0
)
)
(
λ x10 .
x3
(
λ x11 :
ι → ι
.
x0
(
λ x12 .
λ x13 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x14 x15 x16 .
0
)
(
λ x12 .
0
)
0
0
(
λ x12 .
0
)
)
(
setsum
0
0
)
(
λ x11 :
ι →
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
Inj1
0
)
(
x6
0
(
λ x11 x12 .
0
)
(
λ x11 .
0
)
0
)
(
Inj0
0
)
)
)
(
setsum
(
x1
(
λ x9 .
setsum
0
0
)
(
λ x9 :
ι →
ι →
ι → ι
.
x3
(
λ x10 :
ι → ι
.
0
)
0
(
λ x10 :
ι →
ι → ι
.
λ x11 :
ι → ι
.
λ x12 .
0
)
0
0
)
(
x2
(
λ x9 :
ι → ι
.
0
)
(
λ x9 x10 :
(
ι → ι
)
→ ι
.
0
)
)
(
λ x9 .
setsum
0
0
)
)
x5
)
(
λ x9 :
ι →
ι → ι
.
λ x10 :
ι → ι
.
Inj0
)
0
0
)
=
setsum
(
x3
(
λ x9 :
ι → ι
.
Inj0
(
x3
(
λ x10 :
ι → ι
.
x9
0
)
x5
(
λ x10 :
ι →
ι → ι
.
λ x11 :
ι → ι
.
λ x12 .
0
)
(
x6
0
(
λ x10 x11 .
0
)
(
λ x10 .
0
)
0
)
(
Inj0
0
)
)
)
x5
(
λ x9 :
ι →
ι → ι
.
λ x10 :
ι → ι
.
λ x11 .
Inj1
0
)
(
x3
(
λ x9 :
ι → ι
.
setsum
0
(
x3
(
λ x10 :
ι → ι
.
0
)
0
(
λ x10 :
ι →
ι → ι
.
λ x11 :
ι → ι
.
λ x12 .
0
)
0
0
)
)
(
x1
(
λ x9 .
x0
(
λ x10 .
λ x11 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x12 x13 x14 .
0
)
(
λ x10 .
0
)
0
0
(
λ x10 .
0
)
)
(
λ x9 :
ι →
ι →
ι → ι
.
0
)
x5
(
λ x9 .
0
)
)
(
λ x9 :
ι →
ι → ι
.
λ x10 :
ι → ι
.
λ x11 .
Inj1
0
)
0
(
Inj1
(
x2
(
λ x9 :
ι → ι
.
0
)
(
λ x9 x10 :
(
ι → ι
)
→ ι
.
0
)
)
)
)
(
x4
(
λ x9 x10 x11 .
Inj0
0
)
(
λ x9 .
x6
(
x3
(
λ x10 :
ι → ι
.
0
)
0
(
λ x10 :
ι →
ι → ι
.
λ x11 :
ι → ι
.
λ x12 .
0
)
0
0
)
(
λ x10 x11 .
Inj1
0
)
(
λ x10 .
0
)
(
x3
(
λ x10 :
ι → ι
.
0
)
0
(
λ x10 :
ι →
ι → ι
.
λ x11 :
ι → ι
.
λ x12 .
0
)
0
0
)
)
)
)
x7
)
⟶
(
∀ x4 :
(
ι → ι
)
→ ι
.
∀ x5 x6 .
∀ x7 :
(
(
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
x2
(
λ x9 :
ι → ι
.
x9
(
setsum
0
0
)
)
(
λ x9 x10 :
(
ι → ι
)
→ ι
.
x2
(
λ x11 :
ι → ι
.
setsum
0
(
setsum
(
x11
0
)
(
Inj0
0
)
)
)
(
λ x11 x12 :
(
ι → ι
)
→ ι
.
x1
(
λ x13 .
0
)
(
λ x13 :
ι →
ι →
ι → ι
.
x13
(
x0
(
λ x14 .
λ x15 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x16 x17 x18 .
0
)
(
λ x14 .
0
)
0
0
(
λ x14 .
0
)
)
(
x1
(
λ x14 .
0
)
(
λ x14 :
ι →
ι →
ι → ι
.
0
)
0
(
λ x14 .
0
)
)
(
x3
(
λ x14 :
ι → ι
.
0
)
0
(
λ x14 :
ι →
ι → ι
.
λ x15 :
ι → ι
.
λ x16 .
0
)
0
0
)
)
(
x0
(
λ x13 .
λ x14 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x15 x16 x17 .
Inj1
0
)
(
λ x13 .
x13
)
(
setsum
0
0
)
(
x0
(
λ x13 .
λ x14 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x15 x16 x17 .
0
)
(
λ x13 .
0
)
0
0
(
λ x13 .
0
)
)
(
λ x13 .
x1
(
λ x14 .
0
)
(
λ x14 :
ι →
ι →
ι → ι
.
0
)
0
(
λ x14 .
0
)
)
)
(
λ x13 .
0
)
)
)
=
Inj0
(
x4
(
λ x9 .
0
)
)
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
(
ι →
ι → ι
)
→ ι
.
x2
(
λ x9 :
ι → ι
.
x9
0
)
(
λ x9 x10 :
(
ι → ι
)
→ ι
.
x9
(
λ x11 .
0
)
)
=
x5
)
⟶
(
∀ x4 x5 :
ι → ι
.
∀ x6 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
∀ x7 .
x1
(
λ x9 .
x0
(
λ x10 .
λ x11 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x12 x13 x14 .
setsum
0
x13
)
(
λ x10 .
Inj0
(
x3
(
λ x11 :
ι → ι
.
Inj0
0
)
x9
(
λ x11 :
ι →
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
0
)
0
x9
)
)
(
x2
(
λ x10 :
ι → ι
.
0
)
(
λ x10 x11 :
(
ι → ι
)
→ ι
.
setsum
x9
(
x2
(
λ x12 :
ι → ι
.
0
)
(
λ x12 x13 :
(
ι → ι
)
→ ι
.
0
)
)
)
)
(
x1
(
λ x10 .
x3
(
λ x11 :
ι → ι
.
x9
)
0
(
λ x11 :
ι →
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
Inj1
0
)
(
x3
(
λ x11 :
ι → ι
.
0
)
0
(
λ x11 :
ι →
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
0
)
0
0
)
(
x1
(
λ x11 .
0
)
(
λ x11 :
ι →
ι →
ι → ι
.
0
)
0
(
λ x11 .
0
)
)
)
(
λ x10 :
ι →
ι →
ι → ι
.
x0
(
λ x11 .
λ x12 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x13 x14 x15 .
x14
)
(
λ x11 .
x10
0
0
0
)
(
x6
(
λ x11 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x11 .
0
)
)
(
setsum
0
0
)
(
λ x11 .
setsum
0
0
)
)
(
x0
(
λ x10 .
λ x11 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x12 x13 x14 .
x13
)
(
λ x10 .
x1
(
λ x11 .
0
)
(
λ x11 :
ι →
ι →
ι → ι
.
0
)
0
(
λ x11 .
0
)
)
(
x6
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x10 .
0
)
)
(
x3
(
λ x10 :
ι → ι
.
0
)
0
(
λ x10 :
ι →
ι → ι
.
λ x11 :
ι → ι
.
λ x12 .
0
)
0
0
)
(
λ x10 .
0
)
)
(
λ x10 .
0
)
)
(
λ x10 .
x7
)
)
(
λ x9 :
ι →
ι →
ι → ι
.
x6
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
x2
(
λ x11 :
ι → ι
.
x7
)
(
λ x11 x12 :
(
ι → ι
)
→ ι
.
0
)
)
(
λ x10 .
x6
(
λ x11 :
(
ι → ι
)
→
ι → ι
.
x0
(
λ x12 .
λ x13 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x14 x15 x16 .
setsum
0
0
)
(
λ x12 .
0
)
(
x9
0
0
0
)
0
(
λ x12 .
0
)
)
(
λ x11 .
0
)
)
)
0
(
λ x9 .
x2
(
λ x10 :
ι → ι
.
0
)
(
λ x10 x11 :
(
ι → ι
)
→ ι
.
x3
(
λ x12 :
ι → ι
.
x3
(
λ x13 :
ι → ι
.
x1
(
λ x14 .
0
)
(
λ x14 :
ι →
ι →
ι → ι
.
0
)
0
(
λ x14 .
0
)
)
x9
(
λ x13 :
ι →
ι → ι
.
λ x14 :
ι → ι
.
λ x15 .
x1
(
λ x16 .
0
)
(
λ x16 :
ι →
ι →
ι → ι
.
0
)
0
(
λ x16 .
0
)
)
0
(
setsum
0
0
)
)
0
(
λ x12 :
ι →
ι → ι
.
λ x13 :
ι → ι
.
λ x14 .
x14
)
0
0
)
)
=
x2
(
λ x9 :
ι → ι
.
setsum
(
x3
(
λ x10 :
ι → ι
.
x9
(
x2
(
λ x11 :
ι → ι
.
0
)
(
λ x11 x12 :
(
ι → ι
)
→ ι
.
0
)
)
)
(
x2
(
λ x10 :
ι → ι
.
0
)
(
λ x10 x11 :
(
ι → ι
)
→ ι
.
x10
(
λ x12 .
0
)
)
)
(
λ x10 :
ι →
ι → ι
.
λ x11 :
ι → ι
.
λ x12 .
Inj0
0
)
(
x3
(
λ x10 :
ι → ι
.
x2
(
λ x11 :
ι → ι
.
0
)
(
λ x11 x12 :
(
ι → ι
)
→ ι
.
0
)
)
(
setsum
0
0
)
(
λ x10 :
ι →
ι → ι
.
λ x11 :
ι → ι
.
λ x12 .
x0
(
λ x13 .
λ x14 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x15 x16 x17 .
0
)
(
λ x13 .
0
)
0
0
(
λ x13 .
0
)
)
(
x2
(
λ x10 :
ι → ι
.
0
)
(
λ x10 x11 :
(
ι → ι
)
→ ι
.
0
)
)
0
)
0
)
0
)
(
λ x9 x10 :
(
ι → ι
)
→ ι
.
x9
(
λ x11 .
0
)
)
)
⟶
(
∀ x4 .
∀ x5 :
ι →
ι →
(
ι → ι
)
→ ι
.
∀ x6 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι → ι
.
∀ x7 .
x1
(
λ x9 .
setsum
(
Inj1
x7
)
(
setsum
(
x0
(
λ x10 .
λ x11 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x12 x13 x14 .
x12
)
(
λ x10 .
x6
(
λ x11 :
(
ι → ι
)
→
ι → ι
.
0
)
0
)
(
x1
(
λ x10 .
0
)
(
λ x10 :
ι →
ι →
ι → ι
.
0
)
0
(
λ x10 .
0
)
)
0
(
λ x10 .
x6
(
λ x11 :
(
ι → ι
)
→
ι → ι
.
0
)
0
)
)
(
setsum
0
(
x5
0
0
(
λ x10 .
0
)
)
)
)
)
(
λ x9 :
ι →
ι →
ι → ι
.
0
)
(
setsum
0
0
)
(
λ x9 .
x7
)
=
setsum
(
Inj0
(
x5
(
x5
0
(
x3
(
λ x9 :
ι → ι
.
0
)
0
(
λ x9 :
ι →
ι → ι
.
λ x10 :
ι → ι
.
λ x11 .
0
)
0
0
)
(
λ x9 .
setsum
0
0
)
)
(
x1
(
λ x9 .
Inj1
0
)
(
λ x9 :
ι →
ι →
ι → ι
.
x0
(
λ x10 .
λ x11 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x12 x13 x14 .
0
)
(
λ x10 .
0
)
0
0
(
λ x10 .
0
)
)
(
setsum
0
0
)
(
λ x9 .
x3
(
λ x10 :
ι → ι
.
0
)
0
(
λ x10 :
ι →
ι → ι
.
λ x11 :
ι → ι
.
λ x12 .
0
)
0
0
)
)
(
λ x9 .
x9
)
)
)
0
)
⟶
(
∀ x4 :
(
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x5 :
ι →
ι → ι
.
∀ x6 .
∀ x7 :
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
x0
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x11 x12 x13 .
x13
)
(
λ x9 .
setsum
(
x7
(
λ x10 :
(
ι → ι
)
→ ι
.
λ x11 :
ι → ι
.
x11
(
x1
(
λ x12 .
0
)
(
λ x12 :
ι →
ι →
ι → ι
.
0
)
0
(
λ x12 .
0
)
)
)
)
(
x1
(
λ x10 .
x6
)
(
λ x10 :
ι →
ι →
ι → ι
.
x3
(
λ x11 :
ι → ι
.
x9
)
0
(
λ x11 :
ι →
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
Inj0
0
)
(
x2
(
λ x11 :
ι → ι
.
0
)
(
λ x11 x12 :
(
ι → ι
)
→ ι
.
0
)
)
(
x0
(
λ x11 .
λ x12 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x13 x14 x15 .
0
)
(
λ x11 .
0
)
0
0
(
λ x11 .
0
)
)
)
(
x1
(
λ x10 .
0
)
(
λ x10 :
ι →
ι →
ι → ι
.
0
)
0
(
λ x10 .
x9
)
)
(
λ x10 .
setsum
x9
(
x2
(
λ x11 :
ι → ι
.
0
)
(
λ x11 x12 :
(
ι → ι
)
→ ι
.
0
)
)
)
)
)
(
setsum
(
Inj0
(
setsum
(
setsum
0
0
)
(
x1
(
λ x9 .
0
)
(
λ x9 :
ι →
ι →
ι → ι
.
0
)
0
(
λ x9 .
0
)
)
)
)
(
x7
(
λ x9 :
(
ι → ι
)
→ ι
.
λ x10 :
ι → ι
.
0
)
)
)
(
x3
(
λ x9 :
ι → ι
.
Inj1
0
)
0
(
λ x9 :
ι →
ι → ι
.
λ x10 :
ι → ι
.
λ x11 .
x0
(
λ x12 .
λ x13 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x14 x15 .
Inj1
)
(
λ x12 .
x3
(
λ x13 :
ι → ι
.
setsum
0
0
)
(
setsum
0
0
)
(
λ x13 :
ι →
ι → ι
.
λ x14 :
ι → ι
.
λ x15 .
0
)
(
Inj0
0
)
(
setsum
0
0
)
)
0
(
setsum
(
x2
(
λ x12 :
ι → ι
.
0
)
(
λ x12 x13 :
(
ι → ι
)
→ ι
.
0
)
)
x11
)
(
λ x12 .
0
)
)
x6
(
x4
(
λ x9 x10 :
ι → ι
.
λ x11 .
x1
(
λ x12 .
x2
(
λ x13 :
ι → ι
.
0
)
(
λ x13 x14 :
(
ι → ι
)
→ ι
.
0
)
)
(
λ x12 :
ι →
ι →
ι → ι
.
setsum
0
0
)
(
Inj1
0
)
(
λ x12 .
0
)
)
)
)
(
λ x9 .
0
)
=
Inj0
0
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 x6 .
∀ x7 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
x0
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x11 x12 x13 .
Inj0
(
Inj0
(
x0
(
λ x14 .
λ x15 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x16 x17 x18 .
x3
(
λ x19 :
ι → ι
.
0
)
0
(
λ x19 :
ι →
ι → ι
.
λ x20 :
ι → ι
.
λ x21 .
0
)
0
0
)
(
λ x14 .
0
)
0
(
x0
(
λ x14 .
λ x15 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x16 x17 x18 .
0
)
(
λ x14 .
0
)
0
0
(
λ x14 .
0
)
)
(
λ x14 .
x2
(
λ x15 :
ι → ι
.
0
)
(
λ x15 x16 :
(
ι → ι
)
→ ι
.
0
)
)
)
)
)
(
λ x9 .
x5
)
(
Inj0
x5
)
(
Inj0
x6
)
(
λ x9 .
x3
(
λ x10 :
ι → ι
.
setsum
(
x7
x9
(
λ x11 :
ι → ι
.
λ x12 .
x1
(
λ x13 .
0
)
(
λ x13 :
ι →
ι →
ι → ι
.
0
)
0
(
λ x13 .
0
)
)
0
(
x2
(
λ x11 :
ι → ι
.
0
)
(
λ x11 x12 :
(
ι → ι
)
→ ι
.
0
)
)
)
(
setsum
x6
(
Inj1
0
)
)
)
(
x0
(
λ x10 .
λ x11 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x12 x13 x14 .
x3
(
λ x15 :
ι → ι
.
x14
)
x12
(
λ x15 :
ι →
ι → ι
.
λ x16 :
ι → ι
.
λ x17 .
Inj1
0
)
0
x13
)
(
λ x10 .
x9
)
0
(
setsum
(
setsum
0
0
)
0
)
(
λ x10 .
x0
(
λ x11 .
λ x12 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x13 x14 x15 .
x1
(
λ x16 .
0
)
(
λ x16 :
ι →
ι →
ι → ι
.
0
)
0
(
λ x16 .
0
)
)
(
λ x11 .
x11
)
0
x10
(
λ x11 .
x9
)
)
)
(
λ x10 :
ι →
ι → ι
.
λ x11 :
ι → ι
.
λ x12 .
Inj0
x9
)
(
x3
(
λ x10 :
ι → ι
.
x0
(
λ x11 .
λ x12 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x13 x14 x15 .
x12
(
λ x16 :
ι → ι
.
0
)
(
λ x16 .
0
)
0
)
(
λ x11 .
0
)
(
x7
0
(
λ x11 :
ι → ι
.
λ x12 .
0
)
0
0
)
0
(
λ x11 .
Inj1
0
)
)
(
x7
(
x2
(
λ x10 :
ι → ι
.
0
)
(
λ x10 x11 :
(
ι → ι
)
→ ι
.
0
)
)
(
λ x10 :
ι → ι
.
λ x11 .
x9
)
0
(
setsum
0
0
)
)
(
λ x10 :
ι →
ι → ι
.
λ x11 :
ι → ι
.
λ x12 .
x12
)
(
x2
(
λ x10 :
ι → ι
.
Inj1
0
)
(
λ x10 x11 :
(
ι → ι
)
→ ι
.
0
)
)
(
x2
(
λ x10 :
ι → ι
.
0
)
(
λ x10 x11 :
(
ι → ι
)
→ ι
.
x11
(
λ x12 .
0
)
)
)
)
(
x3
(
λ x10 :
ι → ι
.
setsum
(
setsum
0
0
)
x9
)
x9
(
λ x10 :
ι →
ι → ι
.
λ x11 :
ι → ι
.
λ x12 .
0
)
0
(
x7
(
setsum
0
0
)
(
λ x10 :
ι → ι
.
λ x11 .
x7
0
(
λ x12 :
ι → ι
.
λ x13 .
0
)
0
0
)
x5
(
x1
(
λ x10 .
0
)
(
λ x10 :
ι →
ι →
ι → ι
.
0
)
0
(
λ x10 .
0
)
)
)
)
)
=
setsum
(
x1
(
λ x9 .
x3
(
λ x10 :
ι → ι
.
x7
x6
(
λ x11 :
ι → ι
.
λ x12 .
x9
)
(
x10
0
)
(
setsum
0
0
)
)
(
x0
(
λ x10 .
λ x11 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x12 x13 x14 .
x11
(
λ x15 :
ι → ι
.
0
)
(
λ x15 .
0
)
0
)
(
λ x10 .
setsum
0
0
)
x5
(
setsum
0
0
)
(
λ x10 .
setsum
0
0
)
)
(
λ x10 :
ι →
ι → ι
.
λ x11 :
ι → ι
.
λ x12 .
x11
(
x10
0
0
)
)
x9
x9
)
(
λ x9 :
ι →
ι →
ι → ι
.
x7
(
Inj0
(
setsum
0
0
)
)
(
λ x10 :
ι → ι
.
λ x11 .
Inj1
0
)
0
(
x0
(
λ x10 .
λ x11 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x12 x13 x14 .
Inj0
0
)
(
λ x10 .
setsum
0
0
)
0
(
setsum
0
0
)
(
λ x10 .
Inj0
0
)
)
)
x5
(
λ x9 .
0
)
)
(
x3
(
λ x9 :
ι → ι
.
0
)
(
x0
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x11 x12 x13 .
Inj0
0
)
(
λ x9 .
setsum
x6
(
setsum
0
0
)
)
0
(
x2
(
λ x9 :
ι → ι
.
x3
(
λ x10 :
ι → ι
.
0
)
0
(
λ x10 :
ι →
ι → ι
.
λ x11 :
ι → ι
.
λ x12 .
0
)
0
0
)
(
λ x9 x10 :
(
ι → ι
)
→ ι
.
x3
(
λ x11 :
ι → ι
.
0
)
0
(
λ x11 :
ι →
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
0
)
0
0
)
)
(
λ x9 .
setsum
(
x1
(
λ x10 .
0
)
(
λ x10 :
ι →
ι →
ι → ι
.
0
)
0
(
λ x10 .
0
)
)
(
x3
(
λ x10 :
ι → ι
.
0
)
0
(
λ x10 :
ι →
ι → ι
.
λ x11 :
ι → ι
.
λ x12 .
0
)
0
0
)
)
)
(
λ x9 :
ι →
ι → ι
.
λ x10 :
ι → ι
.
λ x11 .
x1
(
λ x12 .
x9
(
x3
(
λ x13 :
ι → ι
.
0
)
0
(
λ x13 :
ι →
ι → ι
.
λ x14 :
ι → ι
.
λ x15 .
0
)
0
0
)
(
Inj0
0
)
)
(
λ x12 :
ι →
ι →
ι → ι
.
x3
(
λ x13 :
ι → ι
.
0
)
0
(
λ x13 :
ι →
ι → ι
.
λ x14 :
ι → ι
.
λ x15 .
0
)
(
x1
(
λ x13 .
0
)
(
λ x13 :
ι →
ι →
ι → ι
.
0
)
0
(
λ x13 .
0
)
)
(
setsum
0
0
)
)
(
x9
0
x11
)
(
λ x12 .
x0
(
λ x13 .
λ x14 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x15 x16 x17 .
x1
(
λ x18 .
0
)
(
λ x18 :
ι →
ι →
ι → ι
.
0
)
0
(
λ x18 .
0
)
)
(
λ x13 .
0
)
(
Inj1
0
)
0
(
λ x13 .
0
)
)
)
x6
(
x0
(
λ x9 .
λ x10 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x11 x12 x13 .
x3
(
λ x14 :
ι → ι
.
setsum
0
0
)
(
x0
(
λ x14 .
λ x15 :
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x16 x17 x18 .
0
)
(
λ x14 .
0
)
0
0
(
λ x14 .
0
)
)
(
λ x14 :
ι →
ι → ι
.
λ x15 :
ι → ι
.
λ x16 .
x14
0
0
)
(
Inj1
0
)
(
Inj1
0
)
)
(
λ x9 .
0
)
(
Inj0
0
)
(
Inj1
0
)
(
λ x9 .
Inj0
(
setsum
0
0
)
)
)
)
)
⟶
False
(proof)
Theorem
ccabb..
:
∀ x0 :
(
(
ι → ι
)
→
(
(
ι →
ι → ι
)
→ ι
)
→ ι
)
→
ι →
ι → ι
.
∀ x1 :
(
ι →
(
ι → ι
)
→ ι
)
→
(
ι →
ι →
ι →
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→
ι → ι
.
∀ x2 :
(
(
ι →
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι →
(
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
.
∀ x3 :
(
(
ι → ι
)
→ ι
)
→
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
(
∀ x4 x5 .
∀ x6 :
(
ι →
ι → ι
)
→ ι
.
∀ x7 :
(
(
ι → ι
)
→ ι
)
→ ι
.
x3
(
λ x9 :
ι → ι
.
0
)
(
λ x9 .
λ x10 :
ι → ι
.
x0
(
λ x11 :
ι → ι
.
λ x12 :
(
ι →
ι → ι
)
→ ι
.
x3
(
λ x13 :
ι → ι
.
x13
(
x12
(
λ x14 x15 .
0
)
)
)
(
λ x13 .
λ x14 :
ι → ι
.
x12
(
λ x15 x16 .
x1
(
λ x17 .
λ x18 :
ι → ι
.
0
)
(
λ x17 x18 x19 x20 .
0
)
(
λ x17 :
ι → ι
.
0
)
0
)
)
)
x9
0
)
=
x0
(
λ x9 :
ι → ι
.
λ x10 :
(
ι →
ι → ι
)
→ ι
.
setsum
0
0
)
(
Inj0
(
x0
(
λ x9 :
ι → ι
.
λ x10 :
(
ι →
ι → ι
)
→ ι
.
Inj1
(
x7
(
λ x11 :
ι → ι
.
0
)
)
)
0
0
)
)
(
setsum
(
x3
(
λ x9 :
ι → ι
.
x9
(
x1
(
λ x10 .
λ x11 :
ι → ι
.
0
)
(
λ x10 x11 x12 x13 .
0
)
(
λ x10 :
ι → ι
.
0
)
0
)
)
(
λ x9 .
λ x10 :
ι → ι
.
0
)
)
0
)
)
⟶
(
∀ x4 .
∀ x5 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
∀ x6 x7 .
x3
(
λ x9 :
ι → ι
.
Inj1
(
setsum
x6
(
setsum
0
0
)
)
)
(
λ x9 .
λ x10 :
ι → ι
.
0
)
=
x5
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
x6
)
)
⟶
(
∀ x4 :
(
ι →
ι →
ι → ι
)
→
ι →
(
ι → ι
)
→ ι
.
∀ x5 x6 :
ι → ι
.
∀ x7 :
ι →
ι → ι
.
x2
(
λ x9 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 :
ι →
(
ι → ι
)
→ ι
.
λ x11 .
λ x12 :
ι → ι
.
0
)
(
x6
(
x1
(
λ x9 .
λ x10 :
ι → ι
.
x3
(
λ x11 :
ι → ι
.
setsum
0
0
)
(
λ x11 .
λ x12 :
ι → ι
.
x12
0
)
)
(
λ x9 x10 x11 x12 .
x12
)
(
λ x9 :
ι → ι
.
0
)
(
setsum
(
setsum
0
0
)
(
x0
(
λ x9 :
ι → ι
.
λ x10 :
(
ι →
ι → ι
)
→ ι
.
0
)
0
0
)
)
)
)
=
setsum
(
x1
(
λ x9 .
λ x10 :
ι → ι
.
0
)
(
λ x9 x10 x11 x12 .
x9
)
(
λ x9 :
ι → ι
.
x0
(
λ x10 :
ι → ι
.
λ x11 :
(
ι →
ι → ι
)
→ ι
.
Inj0
0
)
(
x9
0
)
0
)
(
Inj0
(
x2
(
λ x9 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 :
ι →
(
ι → ι
)
→ ι
.
λ x11 .
λ x12 :
ι → ι
.
0
)
(
x4
(
λ x9 x10 x11 .
0
)
0
(
λ x9 .
0
)
)
)
)
)
0
)
⟶
(
∀ x4 .
∀ x5 :
ι →
ι → ι
.
∀ x6 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x7 .
x2
(
λ x9 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 :
ι →
(
ι → ι
)
→ ι
.
λ x11 .
λ x12 :
ι → ι
.
setsum
(
x9
x11
(
λ x13 :
ι → ι
.
x11
)
)
(
x0
(
λ x13 :
ι → ι
.
λ x14 :
(
ι →
ι → ι
)
→ ι
.
x0
(
λ x15 :
ι → ι
.
λ x16 :
(
ι →
ι → ι
)
→ ι
.
x13
0
)
0
(
x2
(
λ x15 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x16 :
ι →
(
ι → ι
)
→ ι
.
λ x17 .
λ x18 :
ι → ι
.
0
)
0
)
)
0
(
x2
(
λ x13 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x14 :
ι →
(
ι → ι
)
→ ι
.
λ x15 .
λ x16 :
ι → ι
.
setsum
0
0
)
(
x3
(
λ x13 :
ι → ι
.
0
)
(
λ x13 .
λ x14 :
ι → ι
.
0
)
)
)
)
)
x7
=
x7
)
⟶
(
∀ x4 x5 x6 x7 .
x1
(
λ x9 .
λ x10 :
ι → ι
.
setsum
(
x10
x9
)
(
x10
(
x2
(
λ x11 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x12 :
ι →
(
ι → ι
)
→ ι
.
λ x13 .
λ x14 :
ι → ι
.
Inj1
0
)
(
setsum
0
0
)
)
)
)
(
λ x9 x10 x11 x12 .
0
)
(
λ x9 :
ι → ι
.
0
)
(
Inj1
(
Inj1
0
)
)
=
Inj1
(
Inj0
(
x0
(
λ x9 :
ι → ι
.
λ x10 :
(
ι →
ι → ι
)
→ ι
.
Inj0
0
)
(
x1
(
λ x9 .
λ x10 :
ι → ι
.
0
)
(
λ x9 x10 x11 x12 .
x11
)
(
λ x9 :
ι → ι
.
x1
(
λ x10 .
λ x11 :
ι → ι
.
0
)
(
λ x10 x11 x12 x13 .
0
)
(
λ x10 :
ι → ι
.
0
)
0
)
(
x2
(
λ x9 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 :
ι →
(
ι → ι
)
→ ι
.
λ x11 .
λ x12 :
ι → ι
.
0
)
0
)
)
(
x3
(
λ x9 :
ι → ι
.
x0
(
λ x10 :
ι → ι
.
λ x11 :
(
ι →
ι → ι
)
→ ι
.
0
)
0
0
)
(
λ x9 .
λ x10 :
ι → ι
.
Inj1
0
)
)
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 :
ι →
ι →
(
ι → ι
)
→ ι
.
∀ x6 x7 .
x1
(
λ x9 .
λ x10 :
ι → ι
.
setsum
(
x2
(
λ x11 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x12 :
ι →
(
ι → ι
)
→ ι
.
λ x13 .
λ x14 :
ι → ι
.
0
)
0
)
(
x2
(
λ x11 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x12 :
ι →
(
ι → ι
)
→ ι
.
λ x13 .
λ x14 :
ι → ι
.
0
)
0
)
)
(
λ x9 x10 x11 x12 .
x1
(
λ x13 .
λ x14 :
ι → ι
.
x2
(
λ x15 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x16 :
ι →
(
ι → ι
)
→ ι
.
λ x17 .
λ x18 :
ι → ι
.
x3
(
λ x19 :
ι → ι
.
x1
(
λ x20 .
λ x21 :
ι → ι
.
0
)
(
λ x20 x21 x22 x23 .
0
)
(
λ x20 :
ι → ι
.
0
)
0
)
(
λ x19 .
λ x20 :
ι → ι
.
x1
(
λ x21 .
λ x22 :
ι → ι
.
0
)
(
λ x21 x22 x23 x24 .
0
)
(
λ x21 :
ι → ι
.
0
)
0
)
)
(
Inj1
(
Inj0
0
)
)
)
(
λ x13 x14 x15 x16 .
x16
)
(
λ x13 :
ι → ι
.
x10
)
(
x2
(
λ x13 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x14 :
ι →
(
ι → ι
)
→ ι
.
λ x15 .
λ x16 :
ι → ι
.
0
)
x12
)
)
(
λ x9 :
ι → ι
.
x0
(
λ x10 :
ι → ι
.
λ x11 :
(
ι →
ι → ι
)
→ ι
.
x0
(
λ x12 :
ι → ι
.
λ x13 :
(
ι →
ι → ι
)
→ ι
.
x2
(
λ x14 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x15 :
ι →
(
ι → ι
)
→ ι
.
λ x16 .
λ x17 :
ι → ι
.
0
)
(
x0
(
λ x14 :
ι → ι
.
λ x15 :
(
ι →
ι → ι
)
→ ι
.
0
)
0
0
)
)
0
(
Inj1
0
)
)
(
x9
(
Inj1
(
x5
0
0
(
λ x10 .
0
)
)
)
)
(
x1
(
λ x10 .
λ x11 :
ι → ι
.
0
)
(
λ x10 x11 x12 x13 .
x3
(
λ x14 :
ι → ι
.
x3
(
λ x15 :
ι → ι
.
0
)
(
λ x15 .
λ x16 :
ι → ι
.
0
)
)
(
λ x14 .
λ x15 :
ι → ι
.
x14
)
)
(
λ x10 :
ι → ι
.
x9
0
)
(
setsum
(
x2
(
λ x10 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 :
ι →
(
ι → ι
)
→ ι
.
λ x12 .
λ x13 :
ι → ι
.
0
)
0
)
(
Inj0
0
)
)
)
)
(
x3
(
λ x9 :
ι → ι
.
x9
(
x2
(
λ x10 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 :
ι →
(
ι → ι
)
→ ι
.
λ x12 .
λ x13 :
ι → ι
.
x11
0
(
λ x14 .
0
)
)
x7
)
)
(
λ x9 .
λ x10 :
ι → ι
.
x1
(
λ x11 .
λ x12 :
ι → ι
.
x1
(
λ x13 .
λ x14 :
ι → ι
.
x1
(
λ x15 .
λ x16 :
ι → ι
.
0
)
(
λ x15 x16 x17 x18 .
0
)
(
λ x15 :
ι → ι
.
0
)
0
)
(
λ x13 x14 x15 x16 .
0
)
(
λ x13 :
ι → ι
.
Inj1
0
)
x9
)
(
λ x11 x12 x13 x14 .
setsum
(
setsum
0
0
)
x11
)
(
λ x11 :
ι → ι
.
x7
)
x9
)
)
=
setsum
(
x0
(
λ x9 :
ι → ι
.
λ x10 :
(
ι →
ι → ι
)
→ ι
.
setsum
(
x10
(
λ x11 x12 .
x9
0
)
)
(
x9
(
x0
(
λ x11 :
ι → ι
.
λ x12 :
(
ι →
ι → ι
)
→ ι
.
0
)
0
0
)
)
)
(
setsum
(
Inj1
(
x2
(
λ x9 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 :
ι →
(
ι → ι
)
→ ι
.
λ x11 .
λ x12 :
ι → ι
.
0
)
0
)
)
(
x3
(
λ x9 :
ι → ι
.
Inj0
0
)
(
λ x9 .
λ x10 :
ι → ι
.
0
)
)
)
(
x0
(
λ x9 :
ι → ι
.
λ x10 :
(
ι →
ι → ι
)
→ ι
.
x1
(
λ x11 .
λ x12 :
ι → ι
.
setsum
0
0
)
(
λ x11 x12 x13 x14 .
x0
(
λ x15 :
ι → ι
.
λ x16 :
(
ι →
ι → ι
)
→ ι
.
0
)
0
0
)
(
λ x11 :
ι → ι
.
x11
0
)
(
x1
(
λ x11 .
λ x12 :
ι → ι
.
0
)
(
λ x11 x12 x13 x14 .
0
)
(
λ x11 :
ι → ι
.
0
)
0
)
)
x7
(
x5
(
Inj1
0
)
0
(
λ x9 .
Inj0
0
)
)
)
)
0
)
⟶
(
∀ x4 .
∀ x5 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
.
∀ x6 .
∀ x7 :
(
(
ι →
ι → ι
)
→ ι
)
→ ι
.
x0
(
λ x9 :
ι → ι
.
λ x10 :
(
ι →
ι → ι
)
→ ι
.
x3
(
λ x11 :
ι → ι
.
setsum
(
setsum
(
x2
(
λ x12 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x13 :
ι →
(
ι → ι
)
→ ι
.
λ x14 .
λ x15 :
ι → ι
.
0
)
0
)
0
)
(
setsum
(
x1
(
λ x12 .
λ x13 :
ι → ι
.
0
)
(
λ x12 x13 x14 x15 .
0
)
(
λ x12 :
ι → ι
.
0
)
0
)
(
Inj0
0
)
)
)
(
λ x11 .
λ x12 :
ι → ι
.
x11
)
)
(
x1
(
λ x9 .
λ x10 :
ι → ι
.
x2
(
λ x11 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x12 :
ι →
(
ι → ι
)
→ ι
.
λ x13 .
λ x14 :
ι → ι
.
0
)
(
x2
(
λ x11 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x12 :
ι →
(
ι → ι
)
→ ι
.
λ x13 .
λ x14 :
ι → ι
.
x1
(
λ x15 .
λ x16 :
ι → ι
.
0
)
(
λ x15 x16 x17 x18 .
0
)
(
λ x15 :
ι → ι
.
0
)
0
)
x6
)
)
(
λ x9 x10 x11 x12 .
setsum
(
x3
(
λ x13 :
ι → ι
.
Inj1
0
)
(
λ x13 .
λ x14 :
ι → ι
.
setsum
0
0
)
)
(
setsum
(
setsum
0
0
)
(
x0
(
λ x13 :
ι → ι
.
λ x14 :
(
ι →
ι → ι
)
→ ι
.
0
)
0
0
)
)
)
(
λ x9 :
ι → ι
.
x0
(
λ x10 :
ι → ι
.
λ x11 :
(
ι →
ι → ι
)
→ ι
.
x11
(
λ x12 x13 .
0
)
)
(
x3
(
λ x10 :
ι → ι
.
setsum
0
0
)
(
λ x10 .
λ x11 :
ι → ι
.
x2
(
λ x12 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x13 :
ι →
(
ι → ι
)
→ ι
.
λ x14 .
λ x15 :
ι → ι
.
0
)
0
)
)
(
x7
(
λ x10 :
ι →
ι → ι
.
setsum
0
0
)
)
)
(
x2
(
λ x9 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 :
ι →
(
ι → ι
)
→ ι
.
λ x11 .
λ x12 :
ι → ι
.
setsum
(
x2
(
λ x13 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x14 :
ι →
(
ι → ι
)
→ ι
.
λ x15 .
λ x16 :
ι → ι
.
0
)
0
)
0
)
(
setsum
0
0
)
)
)
(
x3
(
λ x9 :
ι → ι
.
x9
0
)
(
λ x9 .
λ x10 :
ι → ι
.
x1
(
λ x11 .
λ x12 :
ι → ι
.
setsum
(
Inj1
0
)
(
x12
0
)
)
(
λ x11 x12 x13 x14 .
0
)
(
λ x11 :
ι → ι
.
x7
(
λ x12 :
ι →
ι → ι
.
setsum
0
0
)
)
(
x3
(
λ x11 :
ι → ι
.
x10
0
)
(
λ x11 .
λ x12 :
ι → ι
.
x1
(
λ x13 .
λ x14 :
ι → ι
.
0
)
(
λ x13 x14 x15 x16 .
0
)
(
λ x13 :
ι → ι
.
0
)
0
)
)
)
)
=
x1
(
λ x9 .
λ x10 :
ι → ι
.
x7
(
λ x11 :
ι →
ι → ι
.
0
)
)
(
λ x9 x10 x11 x12 .
setsum
(
x3
(
λ x13 :
ι → ι
.
0
)
(
λ x13 .
λ x14 :
ι → ι
.
setsum
(
x2
(
λ x15 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x16 :
ι →
(
ι → ι
)
→ ι
.
λ x17 .
λ x18 :
ι → ι
.
0
)
0
)
0
)
)
x11
)
(
λ x9 :
ι → ι
.
setsum
(
x5
(
λ x10 :
(
ι → ι
)
→ ι
.
x10
(
λ x11 .
setsum
0
0
)
)
)
x6
)
(
x0
(
λ x9 :
ι → ι
.
λ x10 :
(
ι →
ι → ι
)
→ ι
.
x3
(
λ x11 :
ι → ι
.
0
)
(
λ x11 .
λ x12 :
ι → ι
.
Inj0
(
x3
(
λ x13 :
ι → ι
.
0
)
(
λ x13 .
λ x14 :
ι → ι
.
0
)
)
)
)
(
Inj1
0
)
0
)
)
⟶
(
∀ x4 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→ ι
.
∀ x5 .
∀ x6 :
(
(
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
∀ x7 .
x0
(
λ x9 :
ι → ι
.
λ x10 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
x1
(
λ x9 .
λ x10 :
ι → ι
.
x0
(
λ x11 :
ι → ι
.
λ x12 :
(
ι →
ι → ι
)
→ ι
.
0
)
0
(
x2
(
λ x11 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x12 :
ι →
(
ι → ι
)
→ ι
.
λ x13 .
λ x14 :
ι → ι
.
0
)
(
Inj0
0
)
)
)
(
λ x9 x10 x11 x12 .
0
)
(
λ x9 :
ι → ι
.
Inj0
(
Inj0
0
)
)
(
x0
(
λ x9 :
ι → ι
.
λ x10 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
Inj1
0
)
x5
)
)
x7
=
setsum
(
x2
(
λ x9 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 :
ι →
(
ι → ι
)
→ ι
.
λ x11 .
λ x12 :
ι → ι
.
x9
(
x0
(
λ x13 :
ι → ι
.
λ x14 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
x12
0
)
0
)
(
λ x13 :
ι → ι
.
x11
)
)
0
)
0
)
⟶
False
(proof)
Theorem
3f9dd..
:
∀ x0 :
(
ι → ι
)
→
ι → ι
.
∀ x1 :
(
ι → ι
)
→
(
ι →
(
ι →
ι → ι
)
→ ι
)
→ ι
.
∀ x2 :
(
(
ι →
ι →
ι →
ι → ι
)
→ ι
)
→
(
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι →
(
ι → ι
)
→
ι → ι
)
→
ι → ι
.
∀ x3 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
(
∀ x4 .
∀ x5 :
ι →
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
∀ x6 x7 .
x3
(
λ x9 :
(
ι → ι
)
→ ι
.
0
)
(
λ x9 .
x0
(
λ x10 .
0
)
x7
)
(
λ x9 .
0
)
=
setsum
0
x4
)
⟶
(
∀ x4 .
∀ x5 :
ι →
(
ι → ι
)
→ ι
.
∀ x6 x7 .
x3
(
λ x9 :
(
ι → ι
)
→ ι
.
x0
(
setsum
0
)
(
setsum
x7
(
x2
(
λ x10 :
ι →
ι →
ι →
ι → ι
.
0
)
(
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 .
λ x12 :
ι → ι
.
λ x13 .
0
)
0
)
)
)
(
λ x9 .
Inj1
x7
)
(
λ x9 .
0
)
=
setsum
(
x2
(
λ x9 :
ι →
ι →
ι →
ι → ι
.
setsum
(
x5
(
x3
(
λ x10 :
(
ι → ι
)
→ ι
.
0
)
(
λ x10 .
0
)
(
λ x10 .
0
)
)
(
λ x10 .
x6
)
)
(
Inj1
(
Inj0
0
)
)
)
(
λ x9 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 .
λ x11 :
ι → ι
.
λ x12 .
0
)
(
Inj1
(
x1
(
λ x9 .
x7
)
(
λ x9 .
λ x10 :
ι →
ι → ι
.
setsum
0
0
)
)
)
)
(
Inj1
0
)
)
⟶
(
∀ x4 .
∀ x5 :
(
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
∀ x6 .
∀ x7 :
(
(
ι → ι
)
→
ι →
ι → ι
)
→
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
x2
(
λ x9 :
ι →
ι →
ι →
ι → ι
.
0
)
(
λ x9 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 .
λ x11 :
ι → ι
.
x0
(
λ x12 .
0
)
)
0
=
setsum
(
x0
(
λ x9 .
setsum
x9
(
x2
(
λ x10 :
ι →
ι →
ι →
ι → ι
.
setsum
0
0
)
(
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 .
λ x12 :
ι → ι
.
λ x13 .
0
)
(
Inj0
0
)
)
)
(
x3
(
λ x9 :
(
ι → ι
)
→ ι
.
0
)
(
λ x9 .
0
)
(
λ x9 .
x9
)
)
)
0
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 x6 x7 .
x2
(
λ x9 :
ι →
ι →
ι →
ι → ι
.
Inj1
(
x9
0
x7
x7
x7
)
)
(
λ x9 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 .
λ x11 :
ι → ι
.
λ x12 .
setsum
0
(
x11
(
x2
(
λ x13 :
ι →
ι →
ι →
ι → ι
.
x2
(
λ x14 :
ι →
ι →
ι →
ι → ι
.
0
)
(
λ x14 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x15 .
λ x16 :
ι → ι
.
λ x17 .
0
)
0
)
(
λ x13 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x14 .
λ x15 :
ι → ι
.
λ x16 .
x15
0
)
(
x11
0
)
)
)
)
0
=
x6
)
⟶
(
∀ x4 :
ι →
ι → ι
.
∀ x5 :
(
(
ι →
ι → ι
)
→ ι
)
→ ι
.
∀ x6 x7 .
x1
(
λ x9 .
x9
)
(
λ x9 .
λ x10 :
ι →
ι → ι
.
x9
)
=
setsum
(
x1
(
λ x9 .
x5
(
λ x10 :
ι →
ι → ι
.
Inj0
x7
)
)
(
λ x9 .
λ x10 :
ι →
ι → ι
.
setsum
(
x1
(
λ x11 .
setsum
0
0
)
(
λ x11 .
λ x12 :
ι →
ι → ι
.
x3
(
λ x13 :
(
ι → ι
)
→ ι
.
0
)
(
λ x13 .
0
)
(
λ x13 .
0
)
)
)
(
Inj1
(
x1
(
λ x11 .
0
)
(
λ x11 .
λ x12 :
ι →
ι → ι
.
0
)
)
)
)
)
0
)
⟶
(
∀ x4 x5 x6 :
ι → ι
.
∀ x7 .
x1
(
λ x9 .
x3
(
λ x10 :
(
ι → ι
)
→ ι
.
x7
)
(
λ x10 .
Inj1
(
x6
0
)
)
(
λ x10 .
setsum
0
(
x1
(
λ x11 .
x7
)
(
λ x11 .
λ x12 :
ι →
ι → ι
.
x11
)
)
)
)
(
λ x9 .
λ x10 :
ι →
ι → ι
.
x9
)
=
x3
(
λ x9 :
(
ι → ι
)
→ ι
.
setsum
(
x6
0
)
(
x6
0
)
)
(
λ x9 .
x6
0
)
(
λ x9 .
setsum
x9
0
)
)
⟶
(
∀ x4 :
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x5 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
∀ x6 :
ι →
ι → ι
.
∀ x7 .
x0
(
λ x9 .
Inj0
0
)
0
=
Inj1
(
Inj1
0
)
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
.
x0
(
λ x9 .
setsum
(
Inj0
x9
)
(
x3
(
λ x10 :
(
ι → ι
)
→ ι
.
0
)
(
λ x10 .
0
)
(
λ x10 .
setsum
0
x6
)
)
)
x4
=
x4
)
⟶
False
(proof)
Theorem
203b5..
:
∀ x0 :
(
(
ι → ι
)
→ ι
)
→
(
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x1 :
(
(
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
)
→
(
ι →
ι →
(
ι → ι
)
→ ι
)
→
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x2 :
(
(
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
)
→ ι
)
→
ι → ι
.
∀ x3 :
(
ι → ι
)
→
(
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
(
∀ x4 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
)
→ ι
.
∀ x5 .
∀ x6 :
ι → ι
.
∀ x7 .
x3
(
λ x9 .
x9
)
(
λ x9 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
(
λ x9 .
0
)
=
x5
)
⟶
(
∀ x4 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x5 :
ι → ι
.
∀ x6 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x7 :
(
ι → ι
)
→
ι → ι
.
x3
(
λ x9 .
x7
(
λ x10 .
x10
)
(
Inj1
(
Inj0
(
x1
(
λ x10 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
(
λ x10 x11 .
λ x12 :
ι → ι
.
0
)
0
(
λ x10 :
ι → ι
.
λ x11 .
0
)
)
)
)
)
(
λ x9 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
Inj1
(
x5
0
)
)
(
x2
(
λ x9 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
Inj0
0
)
)
=
x7
(
λ x9 .
Inj1
(
Inj1
0
)
)
(
Inj0
0
)
)
⟶
(
∀ x4 .
∀ x5 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
(
ι →
ι → ι
)
→
ι →
ι → ι
.
∀ x6 x7 .
x2
(
λ x9 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
Inj0
(
Inj1
(
x5
(
λ x10 .
λ x11 :
ι → ι
.
λ x12 .
x10
)
(
λ x10 x11 .
Inj1
0
)
x6
0
)
)
)
0
=
Inj1
(
Inj0
0
)
)
⟶
(
∀ x4 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
∀ x5 .
∀ x6 :
ι → ι
.
∀ x7 :
ι →
(
ι →
ι → ι
)
→ ι
.
x2
(
λ x9 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
x3
(
λ x10 .
x6
(
setsum
(
x3
(
λ x11 .
0
)
(
λ x11 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
(
λ x11 .
0
)
)
0
)
)
(
λ x10 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
(
λ x10 .
setsum
0
0
)
)
(
Inj0
0
)
=
setsum
(
x4
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 .
0
)
0
(
λ x9 .
setsum
(
x0
(
λ x10 :
ι → ι
.
Inj1
0
)
(
λ x10 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x11 x12 :
ι → ι
.
λ x13 .
setsum
0
0
)
)
(
x1
(
λ x10 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
(
λ x10 x11 .
λ x12 :
ι → ι
.
0
)
0
(
λ x10 :
ι → ι
.
λ x11 .
x2
(
λ x12 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
0
)
0
)
)
)
(
setsum
(
x0
(
λ x9 :
ι → ι
.
Inj0
0
)
(
λ x9 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x10 x11 :
ι → ι
.
λ x12 .
0
)
)
(
x2
(
λ x9 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
x9
(
λ x10 .
0
)
(
λ x10 x11 .
0
)
)
0
)
)
)
(
x0
(
λ x9 :
ι → ι
.
0
)
(
λ x9 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x10 x11 :
ι → ι
.
λ x12 .
x3
(
λ x13 .
Inj0
0
)
(
λ x13 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
x10
0
)
(
λ x13 .
x12
)
)
)
)
⟶
(
∀ x4 :
(
ι → ι
)
→
ι → ι
.
∀ x5 .
∀ x6 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x7 :
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι →
ι →
ι → ι
.
x1
(
λ x9 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
setsum
(
x6
(
x2
(
λ x10 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
x1
(
λ x11 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
(
λ x11 x12 .
λ x13 :
ι → ι
.
0
)
0
(
λ x11 :
ι → ι
.
λ x12 .
0
)
)
0
)
(
λ x10 :
ι → ι
.
x3
(
λ x11 .
setsum
0
0
)
(
λ x11 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
Inj0
0
)
(
λ x11 .
0
)
)
)
0
)
(
λ x9 x10 .
λ x11 :
ι → ι
.
Inj1
x10
)
(
x1
(
λ x9 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
Inj0
x5
)
(
λ x9 x10 .
λ x11 :
ι → ι
.
x7
(
λ x12 :
(
ι → ι
)
→ ι
.
0
)
0
(
setsum
(
x2
(
λ x12 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
0
)
0
)
x10
)
(
x11
(
Inj1
0
)
)
)
0
(
λ x9 :
ι → ι
.
λ x10 .
Inj1
0
)
)
(
λ x9 :
ι → ι
.
λ x10 .
x0
(
λ x11 :
ι → ι
.
x9
0
)
(
λ x11 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x12 x13 :
ι → ι
.
λ x14 .
x14
)
)
=
Inj1
0
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 .
∀ x6 :
(
ι →
ι → ι
)
→
ι → ι
.
∀ x7 .
x1
(
λ x9 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
(
λ x9 x10 .
λ x11 :
ι → ι
.
x0
(
λ x12 :
ι → ι
.
x12
0
)
(
λ x12 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x13 x14 :
ι → ι
.
λ x15 .
x14
(
Inj0
(
x1
(
λ x16 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
(
λ x16 x17 .
λ x18 :
ι → ι
.
0
)
0
(
λ x16 :
ι → ι
.
λ x17 .
0
)
)
)
)
)
(
Inj1
0
)
(
λ x9 :
ι → ι
.
λ x10 .
0
)
=
x0
(
λ x9 :
ι → ι
.
setsum
(
x2
(
λ x10 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
Inj0
0
)
(
x6
(
λ x10 x11 .
x3
(
λ x12 .
0
)
(
λ x12 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
(
λ x12 .
0
)
)
(
setsum
0
0
)
)
)
(
x9
(
setsum
(
setsum
0
0
)
0
)
)
)
(
λ x9 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x10 x11 :
ι → ι
.
λ x12 .
setsum
(
x3
(
λ x13 .
Inj0
x12
)
(
λ x13 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
x11
x12
)
(
λ x13 .
Inj1
x12
)
)
0
)
)
⟶
(
∀ x4 x5 x6 x7 .
x0
(
λ x9 :
ι → ι
.
0
)
(
λ x9 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x10 x11 :
ι → ι
.
λ x12 .
setsum
(
setsum
x12
(
x1
(
λ x13 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→ ι
.
x2
(
λ x14 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
0
)
0
)
(
λ x13 x14 .
λ x15 :
ι → ι
.
x2
(
λ x16 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→ ι
.
0
)
0
)
0
(
λ x13 :
ι → ι
.
λ x14 .
x11
0
)
)
)
0
)
=
Inj0
x5
)
⟶
(
∀ x4 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι →
ι →
ι → ι
.
∀ x5 x6 x7 .
x0
(
λ x9 :
ι → ι
.
0
)
(
λ x9 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x10 x11 :
ι → ι
.
λ x12 .
x3
(
λ x13 .
x13
)
(
λ x13 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
(
λ x13 .
x0
(
λ x14 :
ι → ι
.
Inj0
x13
)
(
λ x14 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
λ x15 x16 :
ι → ι
.
λ x17 .
x3
(
λ x18 .
x3
(
λ x19 .
0
)
(
λ x19 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
(
λ x19 .
0
)
)
(
λ x18 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
x17
)
(
λ x18 .
x15
0
)
)
)
)
=
setsum
(
x3
(
λ x9 .
0
)
(
λ x9 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
x9
(
λ x10 :
ι → ι
.
λ x11 .
Inj0
x7
)
)
(
λ x9 .
x6
)
)
(
x3
(
λ x9 .
x9
)
(
λ x9 :
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
0
)
(
λ x9 .
0
)
)
)
⟶
False
(proof)
Theorem
4d085..
:
∀ x0 :
(
ι → ι
)
→
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→ ι
.
∀ x1 :
(
ι → ι
)
→
(
(
(
(
ι → ι
)
→ ι
)
→ ι
)
→
(
ι →
ι → ι
)
→ ι
)
→ ι
.
∀ x2 :
(
ι → ι
)
→
ι → ι
.
∀ x3 :
(
(
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
)
→
ι →
ι →
ι →
ι → ι
)
→
ι → ι
.
(
∀ x4 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
∀ x5 .
∀ x6 :
(
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
)
→
ι →
(
ι → ι
)
→ ι
.
∀ x7 .
x3
(
λ x9 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 x11 x12 x13 .
Inj1
(
x1
(
λ x14 .
0
)
(
λ x14 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x15 :
ι →
ι → ι
.
0
)
)
)
(
x0
(
λ x9 .
x6
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
λ x11 x12 .
Inj0
(
x2
(
λ x13 .
0
)
0
)
)
0
(
λ x10 .
Inj1
(
Inj0
0
)
)
)
(
λ x9 :
(
ι → ι
)
→ ι
.
x5
)
)
=
setsum
0
x5
)
⟶
(
∀ x4 .
∀ x5 :
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
∀ x6 .
∀ x7 :
ι → ι
.
x3
(
λ x9 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 x11 x12 x13 .
x10
)
(
x5
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 :
ι → ι
.
λ x11 .
x2
(
λ x12 .
0
)
(
x7
(
x7
0
)
)
)
(
setsum
x6
(
x3
(
λ x9 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 x11 x12 x13 .
x12
)
(
setsum
0
0
)
)
)
(
setsum
(
x7
(
x3
(
λ x9 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 x11 x12 x13 .
0
)
0
)
)
(
x5
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 :
ι → ι
.
λ x11 .
x0
(
λ x12 .
0
)
(
λ x12 :
(
ι → ι
)
→ ι
.
0
)
)
0
(
x7
0
)
)
)
)
=
x5
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
λ x10 :
ι → ι
.
λ x11 .
Inj0
0
)
(
Inj0
0
)
(
x1
(
λ x9 .
x6
)
(
λ x9 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 :
ι →
ι → ι
.
setsum
(
x2
(
λ x11 .
Inj1
0
)
(
setsum
0
0
)
)
(
x3
(
λ x11 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x12 x13 x14 x15 .
x13
)
(
x0
(
λ x11 .
0
)
(
λ x11 :
(
ι → ι
)
→ ι
.
0
)
)
)
)
)
)
⟶
(
∀ x4 :
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x5 .
∀ x6 :
ι → ι
.
∀ x7 .
x2
(
λ x9 .
x2
(
λ x10 .
x0
(
λ x11 .
0
)
(
λ x11 :
(
ι → ι
)
→ ι
.
0
)
)
(
x1
(
λ x10 .
Inj1
x7
)
(
λ x10 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 :
ι →
ι → ι
.
x1
(
λ x12 .
Inj1
0
)
(
λ x12 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x13 :
ι →
ι → ι
.
0
)
)
)
)
(
setsum
(
x2
(
λ x9 .
x7
)
0
)
(
Inj1
(
Inj0
(
x4
0
(
λ x9 x10 .
0
)
(
λ x9 .
0
)
)
)
)
)
=
setsum
x7
0
)
⟶
(
∀ x4 :
(
(
ι →
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
∀ x5 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
∀ x6 x7 .
x2
(
λ x9 .
Inj0
x7
)
0
=
x4
(
λ x9 :
ι →
ι → ι
.
x9
x6
(
x2
(
λ x10 .
setsum
x6
0
)
0
)
)
(
λ x9 :
ι → ι
.
λ x10 .
0
)
0
(
x0
(
λ x9 .
x7
)
(
λ x9 :
(
ι → ι
)
→ ι
.
x3
(
λ x10 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 x12 x13 x14 .
0
)
0
)
)
)
⟶
(
∀ x4 :
(
(
(
ι → ι
)
→ ι
)
→
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x5 :
ι → ι
.
∀ x6 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
∀ x7 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
x1
(
λ x9 .
Inj0
(
x6
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
setsum
(
setsum
0
0
)
(
setsum
0
0
)
)
)
)
(
λ x9 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 :
ι →
ι → ι
.
setsum
(
Inj1
0
)
(
x0
(
λ x11 .
x3
(
λ x12 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x13 x14 x15 x16 .
x2
(
λ x17 .
0
)
0
)
0
)
(
λ x11 :
(
ι → ι
)
→ ι
.
x11
(
λ x12 .
x3
(
λ x13 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x14 x15 x16 x17 .
0
)
0
)
)
)
)
=
Inj0
(
x7
(
setsum
(
x0
(
λ x9 .
Inj1
0
)
(
λ x9 :
(
ι → ι
)
→ ι
.
x3
(
λ x10 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x11 x12 x13 x14 .
0
)
0
)
)
(
setsum
(
Inj1
0
)
(
setsum
0
0
)
)
)
(
λ x9 :
ι → ι
.
x7
(
x5
(
x5
0
)
)
(
λ x10 :
ι → ι
.
0
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
(
ι →
ι →
ι → ι
)
→ ι
.
∀ x6 .
∀ x7 :
ι → ι
.
x1
(
λ x9 .
0
)
(
λ x9 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 :
ι →
ι → ι
.
setsum
(
x3
(
λ x11 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x12 x13 x14 x15 .
0
)
(
x7
(
Inj0
0
)
)
)
(
Inj1
(
setsum
0
(
x3
(
λ x11 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x12 x13 x14 x15 .
0
)
0
)
)
)
)
=
setsum
(
x5
(
λ x9 x10 x11 .
x9
)
)
(
x1
(
λ x9 .
0
)
(
λ x9 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x10 :
ι →
ι → ι
.
x1
(
λ x11 .
x0
(
λ x12 .
0
)
(
λ x12 :
(
ι → ι
)
→ ι
.
0
)
)
(
λ x11 :
(
(
ι → ι
)
→ ι
)
→ ι
.
λ x12 :
ι →
ι → ι
.
Inj1
0
)
)
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
∀ x7 :
(
ι → ι
)
→ ι
.
x0
(
λ x9 .
0
)
(
λ x9 :
(
ι → ι
)
→ ι
.
x7
(
λ x10 .
x10
)
)
=
Inj0
(
x0
(
λ x9 .
0
)
(
λ x9 :
(
ι → ι
)
→ ι
.
0
)
)
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
∀ x7 .
x0
(
λ x9 .
x2
(
λ x10 .
0
)
0
)
(
λ x9 :
(
ι → ι
)
→ ι
.
0
)
=
x2
(
λ x9 .
Inj0
(
setsum
(
Inj0
x9
)
0
)
)
(
Inj0
0
)
)
⟶
False
(proof)
Theorem
55e40..
:
∀ x0 :
(
ι → ι
)
→
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x1 :
(
(
(
(
ι →
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→
ι → ι
)
→
ι →
ι →
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x2 :
(
(
ι → ι
)
→
(
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
∀ x3 :
(
ι →
(
ι → ι
)
→ ι
)
→
ι → ι
.
(
∀ x4 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→
ι →
ι → ι
.
∀ x5 :
ι →
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
∀ x6 :
(
ι → ι
)
→ ι
.
∀ x7 :
(
ι →
(
ι → ι
)
→
ι → ι
)
→ ι
.
x3
(
λ x9 .
λ x10 :
ι → ι
.
Inj1
(
Inj0
0
)
)
(
Inj0
(
x7
(
λ x9 .
λ x10 :
ι → ι
.
λ x11 .
x10
(
setsum
0
0
)
)
)
)
=
x6
(
λ x9 .
x0
(
λ x10 .
x6
(
x3
(
λ x11 .
λ x12 :
ι → ι
.
x0
(
λ x13 .
0
)
(
λ x13 :
ι → ι
.
0
)
)
)
)
(
λ x10 :
ι → ι
.
x7
(
λ x11 .
λ x12 :
ι → ι
.
λ x13 .
x10
(
x3
(
λ x14 .
λ x15 :
ι → ι
.
0
)
0
)
)
)
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
ι →
(
(
ι → ι
)
→
ι → ι
)
→ ι
.
∀ x7 :
(
ι → ι
)
→ ι
.
x3
(
λ x9 .
λ x10 :
ι → ι
.
x10
0
)
x5
=
setsum
(
x7
(
λ x9 .
x7
(
λ x10 .
Inj1
x9
)
)
)
(
Inj0
0
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 .
∀ x6 :
ι →
(
ι →
ι → ι
)
→
ι → ι
.
∀ x7 :
ι →
(
ι → ι
)
→
(
ι → ι
)
→ ι
.
x2
(
λ x9 :
ι → ι
.
λ x10 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x11 :
ι →
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
x2
(
λ x14 :
ι → ι
.
λ x15 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x16 :
ι →
ι → ι
.
λ x17 :
ι → ι
.
λ x18 .
x16
(
Inj0
(
x17
0
)
)
0
)
(
x0
(
λ x14 .
0
)
(
λ x14 :
ι → ι
.
0
)
)
(
x1
(
λ x14 :
(
(
ι →
ι → ι
)
→
ι → ι
)
→
ι → ι
.
λ x15 .
Inj1
(
x14
(
λ x16 :
ι →
ι → ι
.
λ x17 .
0
)
0
)
)
0
0
(
λ x14 .
setsum
(
x2
(
λ x15 :
ι → ι
.
λ x16 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x17 :
ι →
ι → ι
.
λ x18 :
ι → ι
.
λ x19 .
0
)
0
0
)
(
x3
(
λ x15 .
λ x16 :
ι → ι
.
0
)
0
)
)
(
λ x14 .
x12
(
setsum
0
0
)
)
)
)
(
x1
(
λ x9 :
(
(
ι →
ι → ι
)
→
ι → ι
)
→
ι → ι
.
λ x10 .
Inj0
0
)
(
x7
(
x1
(
λ x9 :
(
(
ι →
ι → ι
)
→
ι → ι
)
→
ι → ι
.
λ x10 .
0
)
0
(
setsum
0
0
)
(
λ x9 .
x2
(
λ x10 :
ι → ι
.
λ x11 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x12 :
ι →
ι → ι
.
λ x13 :
ι → ι
.
λ x14 .
0
)
0
0
)
(
λ x9 .
0
)
)
(
λ x9 .
x2
(
λ x10 :
ι → ι
.
λ x11 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x12 :
ι →
ι → ι
.
λ x13 :
ι → ι
.
λ x14 .
x3
(
λ x15 .
λ x16 :
ι → ι
.
0
)
0
)
(
x1
(
λ x10 :
(
(
ι →
ι → ι
)
→
ι → ι
)
→
ι → ι
.
λ x11 .
0
)
0
0
(
λ x10 .
0
)
(
λ x10 .
0
)
)
0
)
(
λ x9 .
x2
(
λ x10 :
ι → ι
.
λ x11 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x12 :
ι →
ι → ι
.
λ x13 :
ι → ι
.
λ x14 .
setsum
0
0
)
x9
0
)
)
0
(
λ x9 .
x6
(
setsum
(
x0
(
λ x10 .
0
)
(
λ x10 :
ι → ι
.
0
)
)
(
Inj0
0
)
)
(
λ x10 x11 .
0
)
(
x6
(
x1
(
λ x10 :
(
(
ι →
ι → ι
)
→
ι → ι
)
→
ι → ι
.
λ x11 .
0
)
0
0
(
λ x10 .
0
)
(
λ x10 .
0
)
)
(
λ x10 x11 .
x1
(
λ x12 :
(
(
ι →
ι → ι
)
→
ι → ι
)
→
ι → ι
.
λ x13 .
0
)
0
0
(
λ x12 .
0
)
(
λ x12 .
0
)
)
(
setsum
0
0
)
)
)
(
λ x9 .
x9
)
)
(
setsum
0
(
x4
0
)
)
=
setsum
(
x0
(
λ x9 .
x3
(
λ x10 .
λ x11 :
ι → ι
.
x9
)
(
x7
(
x7
0
(
λ x10 .
0
)
(
λ x10 .
0
)
)
(
λ x10 .
x0
(
λ x11 .
0
)
(
λ x11 :
ι → ι
.
0
)
)
(
λ x10 .
0
)
)
)
(
λ x9 :
ι → ι
.
x5
)
)
(
x4
(
x3
(
λ x9 .
λ x10 :
ι → ι
.
setsum
(
Inj1
0
)
(
setsum
0
0
)
)
(
x1
(
λ x9 :
(
(
ι →
ι → ι
)
→
ι → ι
)
→
ι → ι
.
λ x10 .
0
)
x5
0
(
λ x9 .
Inj1
0
)
(
λ x9 .
x1
(
λ x10 :
(
(
ι →
ι → ι
)
→
ι → ι
)
→
ι → ι
.
λ x11 .
0
)
0
0
(
λ x10 .
0
)
(
λ x10 .
0
)
)
)
)
)
)
⟶
(
∀ x4 :
ι →
(
(
ι → ι
)
→ ι
)
→ ι
.
∀ x5 :
ι → ι
.
∀ x6 x7 .
x2
(
λ x9 :
ι → ι
.
λ x10 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x11 :
ι →
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
x1
(
λ x14 :
(
(
ι →
ι → ι
)
→
ι → ι
)
→
ι → ι
.
λ x15 .
x0
(
λ x16 .
x14
(
λ x17 :
ι →
ι → ι
.
λ x18 .
Inj1
0
)
x15
)
(
λ x16 :
ι → ι
.
Inj1
0
)
)
(
setsum
0
(
x10
(
λ x14 :
ι → ι
.
λ x15 .
x15
)
(
λ x14 .
0
)
)
)
0
(
λ x14 .
x0
(
λ x15 .
setsum
0
(
setsum
0
0
)
)
(
λ x15 :
ι → ι
.
x2
(
λ x16 :
ι → ι
.
λ x17 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x18 :
ι →
ι → ι
.
λ x19 :
ι → ι
.
λ x20 .
x3
(
λ x21 .
λ x22 :
ι → ι
.
0
)
0
)
(
x12
0
)
0
)
)
(
λ x14 .
x14
)
)
0
(
Inj1
0
)
=
x1
(
λ x9 :
(
(
ι →
ι → ι
)
→
ι → ι
)
→
ι → ι
.
λ x10 .
setsum
(
setsum
(
Inj1
(
x1
(
λ x11 :
(
(
ι →
ι → ι
)
→
ι → ι
)
→
ι → ι
.
λ x12 .
0
)
0
0
(
λ x11 .
0
)
(
λ x11 .
0
)
)
)
(
x9
(
λ x11 :
ι →
ι → ι
.
λ x12 .
0
)
(
Inj1
0
)
)
)
x6
)
(
Inj1
(
Inj1
0
)
)
(
x2
(
λ x9 :
ι → ι
.
λ x10 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x11 :
ι →
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
x13
)
(
x4
(
setsum
(
x3
(
λ x9 .
λ x10 :
ι → ι
.
0
)
0
)
(
x0
(
λ x9 .
0
)
(
λ x9 :
ι → ι
.
0
)
)
)
(
λ x9 :
ι → ι
.
x0
(
λ x10 .
setsum
0
0
)
(
λ x10 :
ι → ι
.
Inj1
0
)
)
)
(
x5
(
setsum
(
x3
(
λ x9 .
λ x10 :
ι → ι
.
0
)
0
)
(
x4
0
(
λ x9 :
ι → ι
.
0
)
)
)
)
)
(
λ x9 .
Inj0
(
setsum
(
setsum
(
Inj0
0
)
(
Inj1
0
)
)
(
x3
(
λ x10 .
λ x11 :
ι → ι
.
0
)
0
)
)
)
(
λ x9 .
setsum
0
x6
)
)
⟶
(
∀ x4 :
(
(
ι →
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
∀ x5 :
(
ι →
ι →
ι → ι
)
→ ι
.
∀ x6 .
∀ x7 :
ι → ι
.
x1
(
λ x9 :
(
(
ι →
ι → ι
)
→
ι → ι
)
→
ι → ι
.
λ x10 .
Inj1
0
)
(
x5
(
λ x9 x10 x11 .
x3
(
λ x12 .
λ x13 :
ι → ι
.
setsum
(
x2
(
λ x14 :
ι → ι
.
λ x15 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x16 :
ι →
ι → ι
.
λ x17 :
ι → ι
.
λ x18 .
0
)
0
0
)
0
)
0
)
)
0
(
λ x9 .
x3
(
λ x10 .
λ x11 :
ι → ι
.
x9
)
0
)
(
λ x9 .
0
)
=
x5
(
λ x9 x10 x11 .
setsum
x9
(
x1
(
λ x12 :
(
(
ι →
ι → ι
)
→
ι → ι
)
→
ι → ι
.
λ x13 .
x0
(
λ x14 .
x2
(
λ x15 :
ι → ι
.
λ x16 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x17 :
ι →
ι → ι
.
λ x18 :
ι → ι
.
λ x19 .
0
)
0
0
)
(
λ x14 :
ι → ι
.
Inj0
0
)
)
x9
0
(
λ x12 .
x10
)
(
λ x12 .
0
)
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 :
(
ι →
ι → ι
)
→
ι → ι
.
∀ x6 :
(
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
)
→
(
(
ι → ι
)
→ ι
)
→
(
ι → ι
)
→ ι
.
∀ x7 .
x1
(
λ x9 :
(
(
ι →
ι → ι
)
→
ι → ι
)
→
ι → ι
.
λ x10 .
Inj0
(
setsum
(
x1
(
λ x11 :
(
(
ι →
ι → ι
)
→
ι → ι
)
→
ι → ι
.
λ x12 .
0
)
(
x3
(
λ x11 .
λ x12 :
ι → ι
.
0
)
0
)
(
x1
(
λ x11 :
(
(
ι →
ι → ι
)
→
ι → ι
)
→
ι → ι
.
λ x12 .
0
)
0
0
(
λ x11 .
0
)
(
λ x11 .
0
)
)
(
λ x11 .
0
)
(
λ x11 .
x10
)
)
0
)
)
0
(
Inj1
(
x5
(
λ x9 x10 .
Inj1
0
)
0
)
)
(
λ x9 .
0
)
(
λ x9 .
setsum
x9
(
x2
(
λ x10 :
ι → ι
.
λ x11 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x12 :
ι →
ι → ι
.
λ x13 :
ι → ι
.
λ x14 .
x12
x14
0
)
0
0
)
)
=
Inj1
(
Inj0
(
Inj0
0
)
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 .
∀ x6 :
(
ι → ι
)
→ ι
.
∀ x7 .
x0
(
λ x9 .
x2
(
λ x10 :
ι → ι
.
λ x11 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x12 :
ι →
ι → ι
.
λ x13 :
ι → ι
.
λ x14 .
x0
(
λ x15 .
0
)
(
λ x15 :
ι → ι
.
0
)
)
(
x1
(
λ x10 :
(
(
ι →
ι → ι
)
→
ι → ι
)
→
ι → ι
.
λ x11 .
x9
)
(
x1
(
λ x10 :
(
(
ι →
ι → ι
)
→
ι → ι
)
→
ι → ι
.
λ x11 .
Inj0
0
)
(
x2
(
λ x10 :
ι → ι
.
λ x11 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x12 :
ι →
ι → ι
.
λ x13 :
ι → ι
.
λ x14 .
0
)
0
0
)
x7
(
λ x10 .
x9
)
(
λ x10 .
x1
(
λ x11 :
(
(
ι →
ι → ι
)
→
ι → ι
)
→
ι → ι
.
λ x12 .
0
)
0
0
(
λ x11 .
0
)
(
λ x11 .
0
)
)
)
(
x0
(
λ x10 .
Inj0
0
)
(
λ x10 :
ι → ι
.
0
)
)
(
λ x10 .
0
)
(
λ x10 .
Inj1
(
Inj0
0
)
)
)
(
setsum
(
setsum
(
setsum
0
0
)
(
Inj1
0
)
)
(
Inj0
0
)
)
)
(
λ x9 :
ι → ι
.
x5
)
=
setsum
(
setsum
(
x4
(
x3
(
λ x9 .
λ x10 :
ι → ι
.
x0
(
λ x11 .
0
)
(
λ x11 :
ι → ι
.
0
)
)
(
x0
(
λ x9 .
0
)
(
λ x9 :
ι → ι
.
0
)
)
)
)
(
setsum
(
Inj1
(
x2
(
λ x9 :
ι → ι
.
λ x10 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x11 :
ι →
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
0
)
0
0
)
)
0
)
)
(
Inj1
(
x2
(
λ x9 :
ι → ι
.
λ x10 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x11 :
ι →
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
x12
(
x3
(
λ x14 .
λ x15 :
ι → ι
.
0
)
0
)
)
(
x2
(
λ x9 :
ι → ι
.
λ x10 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x11 :
ι →
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
x3
(
λ x14 .
λ x15 :
ι → ι
.
0
)
0
)
0
0
)
(
Inj0
(
x4
0
)
)
)
)
)
⟶
(
∀ x4 .
∀ x5 :
(
(
ι → ι
)
→ ι
)
→
ι →
(
ι → ι
)
→
ι → ι
.
∀ x6 x7 .
x0
Inj1
(
λ x9 :
ι → ι
.
x6
)
=
setsum
(
x2
(
λ x9 :
ι → ι
.
λ x10 :
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→ ι
.
λ x11 :
ι →
ι → ι
.
λ x12 :
ι → ι
.
λ x13 .
0
)
0
0
)
0
)
⟶
False
(proof)
Theorem
d1c2c..
:
∀ x0 :
(
ι →
(
(
ι →
ι → ι
)
→ ι
)
→ ι
)
→
ι → ι
.
∀ x1 :
(
(
ι → ι
)
→ ι
)
→
(
ι →
ι →
(
ι → ι
)
→
ι → ι
)
→
ι →
(
ι →
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x2 :
(
(
(
ι → ι
)
→
(
ι →
ι → ι
)
→
ι → ι
)
→ ι
)
→
ι →
ι → ι
.
∀ x3 :
(
ι →
(
(
ι →
ι → ι
)
→ ι
)
→
ι → ι
)
→
ι → ι
.
(
∀ x4 :
ι → ι
.
∀ x5 x6 x7 .
x3
(
λ x9 .
λ x10 :
(
ι →
ι → ι
)
→ ι
.
λ x11 .
x3
(
λ x12 .
λ x13 :
(
ι →
ι → ι
)
→ ι
.
λ x14 .
x2
(
λ x15 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→
ι → ι
.
x3
(
λ x16 .
λ x17 :
(
ι →
ι → ι
)
→ ι
.
λ x18 .
x0
(
λ x19 .
λ x20 :
(
ι →
ι → ι
)
→ ι
.
0
)
0
)
x12
)
x11
(
x3
(
λ x15 .
λ x16 :
(
ι →
ι → ι
)
→ ι
.
λ x17 .
x2
(
λ x18 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→
ι → ι
.
0
)
0
0
)
(
x0
(
λ x15 .
λ x16 :
(
ι →
ι → ι
)
→ ι
.
0
)
0
)
)
)
0
)
0
=
x3
(
λ x9 .
λ x10 :
(
ι →
ι → ι
)
→ ι
.
λ x11 .
x0
(
λ x12 .
λ x13 :
(
ι →
ι → ι
)
→ ι
.
x1
(
λ x14 :
ι → ι
.
x13
(
λ x15 x16 .
x0
(
λ x17 .
λ x18 :
(
ι →
ι → ι
)
→ ι
.
0
)
0
)
)
(
λ x14 x15 .
λ x16 :
ι → ι
.
λ x17 .
0
)
(
Inj0
(
x3
(
λ x14 .
λ x15 :
(
ι →
ι → ι
)
→ ι
.
λ x16 .
0
)
0
)
)
(
λ x14 x15 .
setsum
(
x2
(
λ x16 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→
ι → ι
.
0
)
0
0
)
(
Inj1
0
)
)
(
λ x14 .
0
)
0
)
(
x0
(
λ x12 .
λ x13 :
(
ι →
ι → ι
)
→ ι
.
x2
(
λ x14 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→
ι → ι
.
x2
(
λ x15 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→
ι → ι
.
0
)
0
0
)
(
setsum
0
0
)
(
x10
(
λ x14 x15 .
0
)
)
)
x9
)
)
(
Inj1
(
x0
(
λ x9 .
λ x10 :
(
ι →
ι → ι
)
→ ι
.
0
)
x6
)
)
)
⟶
(
∀ x4 x5 .
∀ x6 :
(
(
ι → ι
)
→
ι →
ι → ι
)
→ ι
.
∀ x7 :
ι →
(
ι →
ι → ι
)
→ ι
.
x3
(
λ x9 .
λ x10 :
(
ι →
ι → ι
)
→ ι
.
λ x11 .
x9
)
0
=
x4
)
⟶
(
∀ x4 x5 x6 .
∀ x7 :
(
ι → ι
)
→ ι
.
x2
(
λ x9 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→
ι → ι
.
0
)
(
x2
(
λ x9 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→
ι → ι
.
setsum
(
x1
(
λ x10 :
ι → ι
.
setsum
0
0
)
(
λ x10 x11 .
λ x12 :
ι → ι
.
λ x13 .
x0
(
λ x14 .
λ x15 :
(
ι →
ι → ι
)
→ ι
.
0
)
0
)
(
x7
(
λ x10 .
0
)
)
(
λ x10 x11 .
x10
)
(
λ x10 .
setsum
0
0
)
(
Inj1
0
)
)
(
x2
(
λ x10 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→
ι → ι
.
Inj1
0
)
(
Inj1
0
)
(
x9
(
λ x10 .
0
)
(
λ x10 x11 .
0
)
0
)
)
)
0
(
x1
(
λ x9 :
ι → ι
.
x6
)
(
λ x9 x10 .
λ x11 :
ι → ι
.
λ x12 .
setsum
(
Inj0
0
)
(
setsum
0
0
)
)
(
Inj1
(
x3
(
λ x9 .
λ x10 :
(
ι →
ι → ι
)
→ ι
.
λ x11 .
0
)
0
)
)
(
λ x9 x10 .
0
)
(
λ x9 .
0
)
(
setsum
x5
(
x1
(
λ x9 :
ι → ι
.
0
)
(
λ x9 x10 .
λ x11 :
ι → ι
.
λ x12 .
0
)
0
(
λ x9 x10 .
0
)
(
λ x9 .
0
)
0
)
)
)
)
0
=
x2
(
λ x9 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→
ι → ι
.
x1
(
λ x10 :
ι → ι
.
x6
)
(
λ x10 x11 .
λ x12 :
ι → ι
.
λ x13 .
Inj0
0
)
0
(
λ x10 x11 .
0
)
(
λ x10 .
x3
(
λ x11 .
λ x12 :
(
ι →
ι → ι
)
→ ι
.
λ x13 .
0
)
(
setsum
0
(
x1
(
λ x11 :
ι → ι
.
0
)
(
λ x11 x12 .
λ x13 :
ι → ι
.
λ x14 .
0
)
0
(
λ x11 x12 .
0
)
(
λ x11 .
0
)
0
)
)
)
(
setsum
0
x5
)
)
(
Inj0
0
)
(
Inj1
(
x3
(
λ x9 .
λ x10 :
(
ι →
ι → ι
)
→ ι
.
λ x11 .
x0
(
λ x12 .
λ x13 :
(
ι →
ι → ι
)
→ ι
.
0
)
0
)
(
Inj0
(
x1
(
λ x9 :
ι → ι
.
0
)
(
λ x9 x10 .
λ x11 :
ι → ι
.
λ x12 .
0
)
0
(
λ x9 x10 .
0
)
(
λ x9 .
0
)
0
)
)
)
)
)
⟶
(
∀ x4 :
ι →
ι → ι
.
∀ x5 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→
ι →
ι → ι
.
∀ x6 .
∀ x7 :
(
(
ι →
ι → ι
)
→
ι → ι
)
→
ι → ι
.
x2
(
λ x9 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→
ι → ι
.
0
)
(
x1
(
λ x9 :
ι → ι
.
setsum
(
Inj0
0
)
(
x7
(
λ x10 :
ι →
ι → ι
.
λ x11 .
0
)
0
)
)
(
λ x9 x10 .
λ x11 :
ι → ι
.
λ x12 .
x9
)
(
setsum
(
setsum
(
x5
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x9 x10 .
0
)
0
0
)
(
x0
(
λ x9 .
λ x10 :
(
ι →
ι → ι
)
→ ι
.
0
)
0
)
)
0
)
(
λ x9 x10 .
x0
(
λ x11 .
λ x12 :
(
ι →
ι → ι
)
→ ι
.
x9
)
(
Inj1
x10
)
)
(
λ x9 .
x9
)
(
x7
(
λ x9 :
ι →
ι → ι
.
λ x10 .
0
)
(
Inj1
(
x5
(
λ x9 :
(
ι → ι
)
→
ι → ι
.
0
)
(
λ x9 x10 .
0
)
0
0
)
)
)
)
(
x1
(
λ x9 :
ι → ι
.
0
)
(
λ x9 x10 .
λ x11 :
ι → ι
.
λ x12 .
x0
(
λ x13 .
λ x14 :
(
ι →
ι → ι
)
→ ι
.
0
)
(
x11
(
x3
(
λ x13 .
λ x14 :
(
ι →
ι → ι
)
→ ι
.
λ x15 .
0
)
0
)
)
)
(
x7
(
λ x9 :
ι →
ι → ι
.
λ x10 .
0
)
(
Inj0
(
x2
(
λ x9 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→
ι → ι
.
0
)
0
0
)
)
)
(
λ x9 x10 .
setsum
x9
0
)
(
λ x9 .
setsum
(
Inj0
x9
)
(
setsum
x9
(
x3
(
λ x10 .
λ x11 :
(
ι →
ι → ι
)
→ ι
.
λ x12 .
0
)
0
)
)
)
0
)
=
Inj1
0
)
⟶
(
∀ x4 :
(
(
ι → ι
)
→ ι
)
→
(
ι →
ι → ι
)
→
(
ι → ι
)
→ ι
.
∀ x5 :
ι →
ι →
ι → ι
.
∀ x6 :
(
(
(
ι → ι
)
→
ι → ι
)
→ ι
)
→ ι
.
∀ x7 .
x1
(
λ x9 :
ι → ι
.
x2
(
λ x10 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→
ι → ι
.
x3
(
λ x11 .
λ x12 :
(
ι →
ι → ι
)
→ ι
.
λ x13 .
setsum
0
(
Inj0
0
)
)
(
x9
0
)
)
(
Inj1
(
x6
(
λ x10 :
(
ι → ι
)
→
ι → ι
.
Inj1
0
)
)
)
(
setsum
(
x5
0
(
x5
0
0
0
)
0
)
(
Inj1
0
)
)
)
(
λ x9 x10 .
λ x11 :
ι → ι
.
λ x12 .
x9
)
(
x2
(
λ x9 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→
ι → ι
.
x3
(
λ x10 .
λ x11 :
(
ι →
ι → ι
)
→ ι
.
λ x12 .
x0
(
λ x13 .
λ x14 :
(
ι →
ι → ι
)
→ ι
.
x2
(
λ x15 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→
ι → ι
.
0
)
0
0
)
(
setsum
0
0
)
)
0
)
0
0
)
(
λ x9 x10 .
x1
(
λ x11 :
ι → ι
.
0
)
(
λ x11 x12 .
λ x13 :
ι → ι
.
λ x14 .
x2
(
λ x15 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→
ι → ι
.
0
)
(
setsum
(
x0
(
λ x15 .
λ x16 :
(
ι →
ι → ι
)
→ ι
.
0
)
0
)
x14
)
0
)
(
x3
(
λ x11 .
λ x12 :
(
ι →
ι → ι
)
→ ι
.
λ x13 .
setsum
(
Inj1
0
)
0
)
(
Inj1
0
)
)
(
λ x11 x12 .
0
)
(
λ x11 .
x1
(
λ x12 :
ι → ι
.
setsum
0
0
)
(
λ x12 x13 .
λ x14 :
ι → ι
.
λ x15 .
setsum
(
Inj0
0
)
(
setsum
0
0
)
)
(
Inj0
0
)
(
λ x12 x13 .
x11
)
(
λ x12 .
x11
)
0
)
(
x1
(
λ x11 :
ι → ι
.
x11
0
)
(
λ x11 x12 .
λ x13 :
ι → ι
.
λ x14 .
Inj0
0
)
(
x6
(
λ x11 :
(
ι → ι
)
→
ι → ι
.
setsum
0
0
)
)
(
λ x11 x12 .
x11
)
(
λ x11 .
setsum
x9
(
x0
(
λ x12 .
λ x13 :
(
ι →
ι → ι
)
→ ι
.
0
)
0
)
)
(
Inj1
(
setsum
0
0
)
)
)
)
(
λ x9 .
Inj1
(
setsum
x9
(
x1
(
λ x10 :
ι → ι
.
Inj1
0
)
(
λ x10 x11 .
λ x12 :
ι → ι
.
λ x13 .
setsum
0
0
)
(
x3
(
λ x10 .
λ x11 :
(
ι →
ι → ι
)
→ ι
.
λ x12 .
0
)
0
)
(
λ x10 x11 .
x3
(
λ x12 .
λ x13 :
(
ι →
ι → ι
)
→ ι
.
λ x14 .
0
)
0
)
(
λ x10 .
0
)
0
)
)
)
(
setsum
0
(
x0
(
λ x9 .
λ x10 :
(
ι →
ι → ι
)
→ ι
.
x2
(
λ x11 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→
ι → ι
.
x1
(
λ x12 :
ι → ι
.
0
)
(
λ x12 x13 .
λ x14 :
ι → ι
.
λ x15 .
0
)
0
(
λ x12 x13 .
0
)
(
λ x12 .
0
)
0
)
(
x6
(
λ x11 :
(
ι → ι
)
→
ι → ι
.
0
)
)
(
x0
(
λ x11 .
λ x12 :
(
ι →
ι → ι
)
→ ι
.
0
)
0
)
)
0
)
)
=
x2
(
λ x9 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→
ι → ι
.
setsum
(
Inj1
0
)
(
x9
(
λ x10 .
x2
(
λ x11 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→
ι → ι
.
0
)
(
x1
(
λ x11 :
ι → ι
.
0
)
(
λ x11 x12 .
λ x13 :
ι → ι
.
λ x14 .
0
)
0
(
λ x11 x12 .
0
)
(
λ x11 .
0
)
0
)
(
Inj1
0
)
)
(
λ x10 x11 .
x3
(
λ x12 .
λ x13 :
(
ι →
ι → ι
)
→ ι
.
λ x14 .
Inj1
0
)
(
setsum
0
0
)
)
(
x2
(
λ x10 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→
ι → ι
.
0
)
0
(
setsum
0
0
)
)
)
)
(
Inj1
0
)
(
x0
(
λ x9 .
λ x10 :
(
ι →
ι → ι
)
→ ι
.
x3
(
λ x11 .
λ x12 :
(
ι →
ι → ι
)
→ ι
.
λ x13 .
x11
)
(
x2
(
λ x11 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→
ι → ι
.
0
)
x7
(
setsum
0
0
)
)
)
0
)
)
⟶
(
∀ x4 :
(
ι →
(
ι → ι
)
→ ι
)
→ ι
.
∀ x5 .
∀ x6 :
ι →
ι →
ι →
ι → ι
.
∀ x7 .
x1
(
λ x9 :
ι → ι
.
x6
(
Inj0
(
x0
(
λ x10 .
λ x11 :
(
ι →
ι → ι
)
→ ι
.
setsum
0
0
)
(
x9
0
)
)
)
(
x2
(
λ x10 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→
ι → ι
.
0
)
(
Inj0
(
x0
(
λ x10 .
λ x11 :
(
ι →
ι → ι
)
→ ι
.
0
)
0
)
)
(
setsum
0
0
)
)
0
0
)
(
λ x9 x10 .
λ x11 :
ι → ι
.
λ x12 .
Inj1
0
)
(
x3
(
λ x9 .
λ x10 :
(
ι →
ι → ι
)
→ ι
.
λ x11 .
setsum
0
0
)
(
x6
x5
x7
0
(
x1
(
λ x9 :
ι → ι
.
x7
)
(
λ x9 x10 .
λ x11 :
ι → ι
.
λ x12 .
x2
(
λ x13 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→
ι → ι
.
0
)
0
0
)
(
x4
(
λ x9 .
λ x10 :
ι → ι
.
0
)
)
(
λ x9 x10 .
x6
0
0
0
0
)
(
λ x9 .
x9
)
(
x6
0
0
0
0
)
)
)
)
(
λ x9 .
x1
(
λ x10 :
ι → ι
.
setsum
0
(
Inj1
0
)
)
(
λ x10 x11 .
λ x12 :
ι → ι
.
Inj0
)
0
(
λ x10 .
x1
(
λ x11 :
ι → ι
.
setsum
(
x0
(
λ x12 .
λ x13 :
(
ι →
ι → ι
)
→ ι
.
0
)
0
)
(
x0
(
λ x12 .
λ x13 :
(
ι →
ι → ι
)
→ ι
.
0
)
0
)
)
(
λ x11 x12 .
λ x13 :
ι → ι
.
x3
(
λ x14 .
λ x15 :
(
ι →
ι → ι
)
→ ι
.
λ x16 .
0
)
)
x9
(
λ x11 x12 .
0
)
(
λ x11 .
0
)
)
(
λ x10 .
setsum
x9
(
x1
(
λ x11 :
ι → ι
.
x9
)
(
λ x11 x12 .
λ x13 :
ι → ι
.
λ x14 .
x13
0
)
(
Inj0
0
)
(
λ x11 x12 .
x3
(
λ x13 .
λ x14 :
(
ι →
ι → ι
)
→ ι
.
λ x15 .
0
)
0
)
(
λ x11 .
x10
)
0
)
)
)
(
λ x9 .
0
)
0
=
Inj0
(
Inj1
0
)
)
⟶
(
∀ x4 :
ι → ι
.
∀ x5 :
ι →
ι → ι
.
∀ x6 x7 .
x0
(
λ x9 .
λ x10 :
(
ι →
ι → ι
)
→ ι
.
x9
)
(
x2
(
λ x9 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→
ι → ι
.
setsum
(
setsum
x6
0
)
(
setsum
0
(
setsum
0
0
)
)
)
(
x5
x6
(
Inj1
0
)
)
(
x4
(
setsum
(
Inj0
0
)
x7
)
)
)
=
setsum
0
(
x0
(
λ x9 .
λ x10 :
(
ι →
ι → ι
)
→ ι
.
setsum
(
setsum
(
x0
(
λ x11 .
λ x12 :
(
ι →
ι → ι
)
→ ι
.
0
)
0
)
(
x1
(
λ x11 :
ι → ι
.
0
)
(
λ x11 x12 .
λ x13 :
ι → ι
.
λ x14 .
0
)
0
(
λ x11 x12 .
0
)
(
λ x11 .
0
)
0
)
)
(
x2
(
λ x11 :
(
ι → ι
)
→
(
ι →
ι → ι
)
→
ι → ι
.
x3
(
λ x12 .
λ x13 :
(
ι →
ι → ι
)
→ ι
.
λ x14 .
0
)
0
)
0
(
Inj0
0
)
)
)
0
)
)
⟶
(
∀ x4 .
∀ x5 :
ι → ι
.
∀ x6 :
(
ι → ι
)
→ ι
.
∀ x7 .
x0
(
λ x9 .
λ x10 :
(
ι →
ι → ι
)
→ ι
.
x7
)
(
x3
(
λ x9 .
λ x10 :
(
ι →
ι → ι
)
→ ι
.
λ x11 .
Inj0
0
)
x4
)
=
x7
)
⟶
False
(proof)