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Proofgold Asset
asset id
4bbf24df6dcda83688a3649fb3e171c492732d4caf4c3d8ea972653848ea4fc4
asset hash
edadf69d7738c9c8dbd39820e36d7db06b04d1f34f80fd12e58391e645ca3b34
bday / block
34268
tx
5d266..
preasset
doc published by
Pr4zB..
Param
87bb9..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
not
not
:
ο
→
ο
Definition
fd9fb..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 .
∀ x12 : ο .
(
87bb9..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
⟶
(
x1
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x2
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x3
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x4
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x5
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x6
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x7
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x8
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x9
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x10
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
not
(
x0
x1
x11
)
⟶
not
(
x0
x2
x11
)
⟶
not
(
x0
x3
x11
)
⟶
x0
x4
x11
⟶
not
(
x0
x5
x11
)
⟶
not
(
x0
x6
x11
)
⟶
not
(
x0
x7
x11
)
⟶
x0
x8
x11
⟶
not
(
x0
x9
x11
)
⟶
not
(
x0
x10
x11
)
⟶
x12
)
⟶
x12
Definition
f55c6..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 .
∀ x13 : ο .
(
fd9fb..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
(
x1
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x2
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x3
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x4
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x5
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x6
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x7
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x8
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x9
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x10
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x11
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
x0
x1
x12
⟶
not
(
x0
x2
x12
)
⟶
x0
x3
x12
⟶
not
(
x0
x4
x12
)
⟶
not
(
x0
x5
x12
)
⟶
not
(
x0
x6
x12
)
⟶
not
(
x0
x7
x12
)
⟶
not
(
x0
x8
x12
)
⟶
not
(
x0
x9
x12
)
⟶
not
(
x0
x10
x12
)
⟶
x0
x11
x12
⟶
x13
)
⟶
x13
Param
f1c88..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Definition
7aa0e..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 .
∀ x12 : ο .
(
f1c88..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
⟶
(
x1
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x2
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x3
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x4
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x5
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x6
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x7
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x8
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x9
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x10
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
x0
x1
x11
⟶
not
(
x0
x2
x11
)
⟶
not
(
x0
x3
x11
)
⟶
not
(
x0
x4
x11
)
⟶
not
(
x0
x5
x11
)
⟶
not
(
x0
x6
x11
)
⟶
not
(
x0
x7
x11
)
⟶
x0
x8
x11
⟶
not
(
x0
x9
x11
)
⟶
not
(
x0
x10
x11
)
⟶
x12
)
⟶
x12
Param
6f07c..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Definition
0e688..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 .
∀ x12 : ο .
(
6f07c..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
⟶
(
x1
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x2
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x3
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x4
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x5
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x6
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x7
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x8
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x9
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x10
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
not
(
x0
x1
x11
)
⟶
x0
x2
x11
⟶
not
(
x0
x3
x11
)
⟶
not
(
x0
x4
x11
)
⟶
not
(
x0
x5
x11
)
⟶
not
(
x0
x6
x11
)
⟶
not
(
x0
x7
x11
)
⟶
x0
x8
x11
⟶
not
(
x0
x9
x11
)
⟶
not
(
x0
x10
x11
)
⟶
x12
)
⟶
x12
Definition
c1824..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 .
∀ x12 : ο .
(
f1c88..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
⟶
(
x1
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x2
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x3
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x4
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x5
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x6
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x7
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x8
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x9
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x10
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
not
(
x0
x1
x11
)
⟶
not
(
x0
x2
x11
)
⟶
x0
x3
x11
⟶
not
(
x0
x4
x11
)
⟶
not
(
x0
x5
x11
)
⟶
not
(
x0
x6
x11
)
⟶
not
(
x0
x7
x11
)
⟶
x0
x8
x11
⟶
not
(
x0
x9
x11
)
⟶
not
(
x0
x10
x11
)
⟶
x12
)
⟶
x12
Definition
79b8d..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 .
∀ x13 : ο .
(
c1824..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
(
x1
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x2
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x3
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x4
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x5
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x6
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x7
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x8
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x9
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x10
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x11
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
x0
x1
x12
⟶
not
(
x0
x2
x12
)
⟶
not
(
x0
x3
x12
)
⟶
not
(
x0
x4
x12
)
⟶
x0
x5
x12
⟶
not
(
x0
x6
x12
)
⟶
not
(
x0
x7
x12
)
⟶
not
(
x0
x8
x12
)
⟶
not
(
x0
x9
x12
)
⟶
not
(
x0
x10
x12
)
⟶
x0
x11
x12
⟶
x13
)
⟶
x13
Definition
df3c6..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 .
∀ x12 : ο .
(
f1c88..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
⟶
(
x1
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x2
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x3
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x4
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x5
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x6
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x7
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x8
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x9
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x10
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
not
(
x0
x1
x11
)
⟶
x0
x2
x11
⟶
x0
x3
x11
⟶
not
(
x0
x4
x11
)
⟶
not
(
x0
x5
x11
)
⟶
not
(
x0
x6
x11
)
⟶
not
(
x0
x7
x11
)
⟶
x0
x8
x11
⟶
not
(
x0
x9
x11
)
⟶
not
(
x0
x10
x11
)
⟶
x12
)
⟶
x12
Definition
2e358..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 .
∀ x13 : ο .
(
df3c6..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
(
x1
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x2
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x3
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x4
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x5
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x6
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x7
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x8
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x9
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x10
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x11
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
x0
x1
x12
⟶
not
(
x0
x2
x12
)
⟶
not
(
x0
x3
x12
)
⟶
not
(
x0
x4
x12
)
⟶
not
(
x0
x5
x12
)
⟶
x0
x6
x12
⟶
not
(
x0
x7
x12
)
⟶
not
(
x0
x8
x12
)
⟶
not
(
x0
x9
x12
)
⟶
not
(
x0
x10
x12
)
⟶
x0
x11
x12
⟶
x13
)
⟶
x13
Definition
91ad9..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 .
∀ x13 : ο .
(
df3c6..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
(
x1
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x2
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x3
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x4
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x5
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x6
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x7
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x8
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x9
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x10
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x11
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
x0
x1
x12
⟶
not
(
x0
x2
x12
)
⟶
not
(
x0
x3
x12
)
⟶
not
(
x0
x4
x12
)
⟶
x0
x5
x12
⟶
x0
x6
x12
⟶
not
(
x0
x7
x12
)
⟶
not
(
x0
x8
x12
)
⟶
not
(
x0
x9
x12
)
⟶
not
(
x0
x10
x12
)
⟶
x0
x11
x12
⟶
x13
)
⟶
x13
Param
d8b5d..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Definition
c7c61..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 .
∀ x12 : ο .
(
d8b5d..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
⟶
(
x1
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x2
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x3
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x4
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x5
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x6
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x7
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x8
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x9
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x10
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
not
(
x0
x1
x11
)
⟶
not
(
x0
x2
x11
)
⟶
x0
x3
x11
⟶
not
(
x0
x4
x11
)
⟶
not
(
x0
x5
x11
)
⟶
not
(
x0
x6
x11
)
⟶
not
(
x0
x7
x11
)
⟶
x0
x8
x11
⟶
not
(
x0
x9
x11
)
⟶
not
(
x0
x10
x11
)
⟶
x12
)
⟶
x12
Param
55171..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Definition
e5b9c..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 .
∀ x12 : ο .
(
55171..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
⟶
(
x1
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x2
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x3
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x4
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x5
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x6
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x7
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x8
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x9
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x10
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
x0
x1
x11
⟶
x0
x2
x11
⟶
x0
x3
x11
⟶
not
(
x0
x4
x11
)
⟶
not
(
x0
x5
x11
)
⟶
not
(
x0
x6
x11
)
⟶
not
(
x0
x7
x11
)
⟶
x0
x8
x11
⟶
not
(
x0
x9
x11
)
⟶
not
(
x0
x10
x11
)
⟶
x12
)
⟶
x12
Param
1465e..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Definition
ea5d0..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 .
∀ x12 : ο .
(
1465e..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
⟶
(
x1
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x2
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x3
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x4
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x5
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x6
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x7
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x8
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x9
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x10
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
not
(
x0
x1
x11
)
⟶
not
(
x0
x2
x11
)
⟶
x0
x3
x11
⟶
not
(
x0
x4
x11
)
⟶
not
(
x0
x5
x11
)
⟶
not
(
x0
x6
x11
)
⟶
not
(
x0
x7
x11
)
⟶
x0
x8
x11
⟶
not
(
x0
x9
x11
)
⟶
not
(
x0
x10
x11
)
⟶
x12
)
⟶
x12
Definition
7f80f..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 .
∀ x12 : ο .
(
1465e..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
⟶
(
x1
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x2
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x3
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x4
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x5
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x6
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x7
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x8
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x9
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x10
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
not
(
x0
x1
x11
)
⟶
x0
x2
x11
⟶
x0
x3
x11
⟶
not
(
x0
x4
x11
)
⟶
not
(
x0
x5
x11
)
⟶
not
(
x0
x6
x11
)
⟶
not
(
x0
x7
x11
)
⟶
x0
x8
x11
⟶
not
(
x0
x9
x11
)
⟶
not
(
x0
x10
x11
)
⟶
x12
)
⟶
x12
Definition
f1399..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 .
∀ x12 : ο .
(
1465e..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
⟶
(
x1
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x2
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x3
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x4
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x5
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x6
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x7
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x8
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x9
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x10
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
x0
x1
x11
⟶
x0
x2
x11
⟶
x0
x3
x11
⟶
not
(
x0
x4
x11
)
⟶
not
(
x0
x5
x11
)
⟶
not
(
x0
x6
x11
)
⟶
not
(
x0
x7
x11
)
⟶
x0
x8
x11
⟶
not
(
x0
x9
x11
)
⟶
not
(
x0
x10
x11
)
⟶
x12
)
⟶
x12
Param
97406..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Definition
0a04b..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 .
∀ x12 : ο .
(
97406..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
⟶
(
x1
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x2
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x3
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x4
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x5
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x6
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x7
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x8
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x9
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x10
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
not
(
x0
x1
x11
)
⟶
not
(
x0
x2
x11
)
⟶
not
(
x0
x3
x11
)
⟶
x0
x4
x11
⟶
not
(
x0
x5
x11
)
⟶
not
(
x0
x6
x11
)
⟶
not
(
x0
x7
x11
)
⟶
x0
x8
x11
⟶
not
(
x0
x9
x11
)
⟶
not
(
x0
x10
x11
)
⟶
x12
)
⟶
x12
Definition
aec6c..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 .
∀ x12 : ο .
(
97406..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
⟶
(
x1
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x2
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x3
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x4
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x5
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x6
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x7
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x8
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x9
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x10
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
x0
x1
x11
⟶
not
(
x0
x2
x11
)
⟶
not
(
x0
x3
x11
)
⟶
x0
x4
x11
⟶
not
(
x0
x5
x11
)
⟶
not
(
x0
x6
x11
)
⟶
not
(
x0
x7
x11
)
⟶
x0
x8
x11
⟶
not
(
x0
x9
x11
)
⟶
not
(
x0
x10
x11
)
⟶
x12
)
⟶
x12
Param
4b1cb..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Definition
b50f9..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 .
∀ x12 : ο .
(
4b1cb..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
⟶
(
x1
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x2
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x3
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x4
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x5
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x6
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x7
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x8
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x9
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x10
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
x0
x1
x11
⟶
x0
x2
x11
⟶
not
(
x0
x3
x11
)
⟶
x0
x4
x11
⟶
not
(
x0
x5
x11
)
⟶
not
(
x0
x6
x11
)
⟶
not
(
x0
x7
x11
)
⟶
x0
x8
x11
⟶
not
(
x0
x9
x11
)
⟶
not
(
x0
x10
x11
)
⟶
x12
)
⟶
x12
Param
6d791..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Definition
cc1e8..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 .
∀ x12 : ο .
(
6d791..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
⟶
(
x1
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x2
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x3
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x4
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x5
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x6
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x7
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x8
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x9
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x10
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
not
(
x0
x1
x11
)
⟶
x0
x2
x11
⟶
not
(
x0
x3
x11
)
⟶
not
(
x0
x4
x11
)
⟶
x0
x5
x11
⟶
not
(
x0
x6
x11
)
⟶
not
(
x0
x7
x11
)
⟶
x0
x8
x11
⟶
not
(
x0
x9
x11
)
⟶
not
(
x0
x10
x11
)
⟶
x12
)
⟶
x12
Definition
ade95..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 .
∀ x12 : ο .
(
6f07c..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
⟶
(
x1
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x2
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x3
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x4
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x5
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x6
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x7
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x8
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x9
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x10
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
x0
x1
x11
⟶
x0
x2
x11
⟶
not
(
x0
x3
x11
)
⟶
not
(
x0
x4
x11
)
⟶
x0
x5
x11
⟶
not
(
x0
x6
x11
)
⟶
not
(
x0
x7
x11
)
⟶
x0
x8
x11
⟶
not
(
x0
x9
x11
)
⟶
not
(
x0
x10
x11
)
⟶
x12
)
⟶
x12
Param
7c588..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Definition
5ed8e..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 .
∀ x12 : ο .
(
7c588..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
⟶
(
x1
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x2
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x3
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x4
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x5
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x6
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x7
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x8
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x9
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x10
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
not
(
x0
x1
x11
)
⟶
not
(
x0
x2
x11
)
⟶
x0
x3
x11
⟶
not
(
x0
x4
x11
)
⟶
not
(
x0
x5
x11
)
⟶
not
(
x0
x6
x11
)
⟶
not
(
x0
x7
x11
)
⟶
x0
x8
x11
⟶
not
(
x0
x9
x11
)
⟶
not
(
x0
x10
x11
)
⟶
x12
)
⟶
x12
Param
133c1..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Definition
efc7e..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 .
∀ x12 : ο .
(
133c1..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
⟶
(
x1
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x2
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x3
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x4
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x5
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x6
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x7
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x8
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x9
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x10
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
x0
x1
x11
⟶
x0
x2
x11
⟶
not
(
x0
x3
x11
)
⟶
not
(
x0
x4
x11
)
⟶
x0
x5
x11
⟶
not
(
x0
x6
x11
)
⟶
not
(
x0
x7
x11
)
⟶
x0
x8
x11
⟶
not
(
x0
x9
x11
)
⟶
not
(
x0
x10
x11
)
⟶
x12
)
⟶
x12
Param
51ac7..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Definition
8fef1..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 .
∀ x12 : ο .
(
51ac7..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
⟶
(
x1
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x2
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x3
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x4
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x5
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x6
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x7
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x8
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x9
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x10
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
not
(
x0
x1
x11
)
⟶
x0
x2
x11
⟶
not
(
x0
x3
x11
)
⟶
not
(
x0
x4
x11
)
⟶
not
(
x0
x5
x11
)
⟶
not
(
x0
x6
x11
)
⟶
not
(
x0
x7
x11
)
⟶
x0
x8
x11
⟶
not
(
x0
x9
x11
)
⟶
not
(
x0
x10
x11
)
⟶
x12
)
⟶
x12
Param
15aa1..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Definition
418c9..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 .
∀ x12 : ο .
(
15aa1..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
⟶
(
x1
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x2
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x3
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x4
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x5
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x6
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x7
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x8
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x9
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x10
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
x0
x1
x11
⟶
x0
x2
x11
⟶
not
(
x0
x3
x11
)
⟶
x0
x4
x11
⟶
not
(
x0
x5
x11
)
⟶
not
(
x0
x6
x11
)
⟶
not
(
x0
x7
x11
)
⟶
x0
x8
x11
⟶
not
(
x0
x9
x11
)
⟶
not
(
x0
x10
x11
)
⟶
x12
)
⟶
x12
Param
7683c..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Definition
f3a4c..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 .
∀ x12 : ο .
(
7683c..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
⟶
(
x1
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x2
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x3
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x4
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x5
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x6
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x7
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x8
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x9
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x10
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
not
(
x0
x1
x11
)
⟶
not
(
x0
x2
x11
)
⟶
x0
x3
x11
⟶
not
(
x0
x4
x11
)
⟶
not
(
x0
x5
x11
)
⟶
not
(
x0
x6
x11
)
⟶
not
(
x0
x7
x11
)
⟶
x0
x8
x11
⟶
not
(
x0
x9
x11
)
⟶
not
(
x0
x10
x11
)
⟶
x12
)
⟶
x12
Param
07f55..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Definition
8dc75..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 .
∀ x12 : ο .
(
07f55..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
⟶
(
x1
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x2
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x3
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x4
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x5
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x6
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x7
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x8
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x9
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x10
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
not
(
x0
x1
x11
)
⟶
not
(
x0
x2
x11
)
⟶
x0
x3
x11
⟶
not
(
x0
x4
x11
)
⟶
not
(
x0
x5
x11
)
⟶
not
(
x0
x6
x11
)
⟶
not
(
x0
x7
x11
)
⟶
x0
x8
x11
⟶
not
(
x0
x9
x11
)
⟶
not
(
x0
x10
x11
)
⟶
x12
)
⟶
x12
Param
e68b8..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Definition
36e27..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 .
∀ x12 : ο .
(
e68b8..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
⟶
(
x1
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x2
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x3
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x4
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x5
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x6
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x7
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x8
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x9
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x10
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
x0
x1
x11
⟶
not
(
x0
x2
x11
)
⟶
not
(
x0
x3
x11
)
⟶
not
(
x0
x4
x11
)
⟶
not
(
x0
x5
x11
)
⟶
not
(
x0
x6
x11
)
⟶
not
(
x0
x7
x11
)
⟶
x0
x8
x11
⟶
not
(
x0
x9
x11
)
⟶
not
(
x0
x10
x11
)
⟶
x12
)
⟶
x12
Param
5bc1a..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Definition
8dbd3..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 .
∀ x12 : ο .
(
5bc1a..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
⟶
(
x1
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x2
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x3
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x4
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x5
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x6
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x7
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x8
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x9
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x10
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
x0
x1
x11
⟶
not
(
x0
x2
x11
)
⟶
not
(
x0
x3
x11
)
⟶
not
(
x0
x4
x11
)
⟶
not
(
x0
x5
x11
)
⟶
not
(
x0
x6
x11
)
⟶
not
(
x0
x7
x11
)
⟶
x0
x8
x11
⟶
not
(
x0
x9
x11
)
⟶
not
(
x0
x10
x11
)
⟶
x12
)
⟶
x12
Param
02f40..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Definition
0ed40..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 .
∀ x12 : ο .
(
02f40..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
⟶
(
x1
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x2
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x3
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x4
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x5
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x6
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x7
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x8
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x9
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x10
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
not
(
x0
x1
x11
)
⟶
not
(
x0
x2
x11
)
⟶
x0
x3
x11
⟶
not
(
x0
x4
x11
)
⟶
not
(
x0
x5
x11
)
⟶
not
(
x0
x6
x11
)
⟶
not
(
x0
x7
x11
)
⟶
x0
x8
x11
⟶
not
(
x0
x9
x11
)
⟶
not
(
x0
x10
x11
)
⟶
x12
)
⟶
x12
Definition
76168..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 .
∀ x12 : ο .
(
5bc1a..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
⟶
(
x1
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x2
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x3
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x4
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x5
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x6
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x7
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x8
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x9
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x10
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
not
(
x0
x1
x11
)
⟶
not
(
x0
x2
x11
)
⟶
x0
x3
x11
⟶
not
(
x0
x4
x11
)
⟶
not
(
x0
x5
x11
)
⟶
not
(
x0
x6
x11
)
⟶
not
(
x0
x7
x11
)
⟶
x0
x8
x11
⟶
not
(
x0
x9
x11
)
⟶
not
(
x0
x10
x11
)
⟶
x12
)
⟶
x12
Definition
e4d70..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 .
∀ x13 : ο .
(
76168..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
(
x1
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x2
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x3
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x4
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x5
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x6
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x7
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x8
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x9
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x10
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x11
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
x0
x1
x12
⟶
not
(
x0
x2
x12
)
⟶
not
(
x0
x3
x12
)
⟶
not
(
x0
x4
x12
)
⟶
x0
x5
x12
⟶
not
(
x0
x6
x12
)
⟶
not
(
x0
x7
x12
)
⟶
not
(
x0
x8
x12
)
⟶
not
(
x0
x9
x12
)
⟶
not
(
x0
x10
x12
)
⟶
x0
x11
x12
⟶
x13
)
⟶
x13
Definition
07080..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 .
∀ x13 : ο .
(
76168..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
(
x1
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x2
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x3
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x4
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x5
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x6
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x7
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x8
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x9
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x10
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
(
x11
=
x12
⟶
∀ x14 : ο .
x14
)
⟶
x0
x1
x12
⟶
not
(
x0
x2
x12
)
⟶
not
(
x0
x3
x12
)
⟶
not
(
x0
x4
x12
)
⟶
x0
x5
x12
⟶
x0
x6
x12
⟶
not
(
x0
x7
x12
)
⟶
not
(
x0
x8
x12
)
⟶
not
(
x0
x9
x12
)
⟶
not
(
x0
x10
x12
)
⟶
x0
x11
x12
⟶
x13
)
⟶
x13
Definition
6799e..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 .
∀ x14 : ο .
(
07080..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
(
x1
=
x13
⟶
∀ x15 : ο .
x15
)
⟶
(
x2
=
x13
⟶
∀ x15 : ο .
x15
)
⟶
(
x3
=
x13
⟶
∀ x15 : ο .
x15
)
⟶
(
x4
=
x13
⟶
∀ x15 : ο .
x15
)
⟶
(
x5
=
x13
⟶
∀ x15 : ο .
x15
)
⟶
(
x6
=
x13
⟶
∀ x15 : ο .
x15
)
⟶
(
x7
=
x13
⟶
∀ x15 : ο .
x15
)
⟶
(
x8
=
x13
⟶
∀ x15 : ο .
x15
)
⟶
(
x9
=
x13
⟶
∀ x15 : ο .
x15
)
⟶
(
x10
=
x13
⟶
∀ x15 : ο .
x15
)
⟶
(
x11
=
x13
⟶
∀ x15 : ο .
x15
)
⟶
(
x12
=
x13
⟶
∀ x15 : ο .
x15
)
⟶
x0
x1
x13
⟶
x0
x2
x13
⟶
not
(
x0
x3
x13
)
⟶
x0
x4
x13
⟶
not
(
x0
x5
x13
)
⟶
not
(
x0
x6
x13
)
⟶
not
(
x0
x7
x13
)
⟶
not
(
x0
x8
x13
)
⟶
not
(
x0
x9
x13
)
⟶
not
(
x0
x10
x13
)
⟶
x0
x11
x13
⟶
not
(
x0
x12
x13
)
⟶
x14
)
⟶
x14
Param
b1def..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Definition
df932..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 .
∀ x12 : ο .
(
b1def..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
⟶
(
x1
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x2
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x3
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x4
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x5
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x6
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x7
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x8
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x9
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x10
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
x0
x1
x11
⟶
x0
x2
x11
⟶
x0
x3
x11
⟶
not
(
x0
x4
x11
)
⟶
not
(
x0
x5
x11
)
⟶
not
(
x0
x6
x11
)
⟶
not
(
x0
x7
x11
)
⟶
x0
x8
x11
⟶
not
(
x0
x9
x11
)
⟶
not
(
x0
x10
x11
)
⟶
x12
)
⟶
x12
Definition
8aed1..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 .
∀ x12 : ο .
(
5bc1a..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
⟶
(
x1
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x2
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x3
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x4
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x5
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x6
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x7
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x8
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x9
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x10
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
x0
x1
x11
⟶
x0
x2
x11
⟶
x0
x3
x11
⟶
not
(
x0
x4
x11
)
⟶
not
(
x0
x5
x11
)
⟶
not
(
x0
x6
x11
)
⟶
not
(
x0
x7
x11
)
⟶
x0
x8
x11
⟶
not
(
x0
x9
x11
)
⟶
not
(
x0
x10
x11
)
⟶
x12
)
⟶
x12
Param
8befb..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Definition
9f9d1..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 .
∀ x12 : ο .
(
8befb..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
⟶
(
x1
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x2
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x3
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x4
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x5
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x6
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x7
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x8
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x9
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x10
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
x0
x1
x11
⟶
x0
x2
x11
⟶
x0
x3
x11
⟶
not
(
x0
x4
x11
)
⟶
not
(
x0
x5
x11
)
⟶
not
(
x0
x6
x11
)
⟶
not
(
x0
x7
x11
)
⟶
x0
x8
x11
⟶
not
(
x0
x9
x11
)
⟶
not
(
x0
x10
x11
)
⟶
x12
)
⟶
x12
Param
3d118..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Definition
be6eb..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 .
∀ x12 : ο .
(
3d118..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
⟶
(
x1
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x2
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x3
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x4
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x5
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x6
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x7
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x8
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x9
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x10
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
x0
x1
x11
⟶
x0
x2
x11
⟶
x0
x3
x11
⟶
not
(
x0
x4
x11
)
⟶
not
(
x0
x5
x11
)
⟶
not
(
x0
x6
x11
)
⟶
not
(
x0
x7
x11
)
⟶
x0
x8
x11
⟶
not
(
x0
x9
x11
)
⟶
not
(
x0
x10
x11
)
⟶
x12
)
⟶
x12
Param
856bc..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Definition
913ca..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 .
∀ x12 : ο .
(
856bc..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
⟶
(
x1
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x2
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x3
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x4
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x5
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x6
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x7
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x8
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x9
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x10
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
x0
x1
x11
⟶
x0
x2
x11
⟶
x0
x3
x11
⟶
not
(
x0
x4
x11
)
⟶
not
(
x0
x5
x11
)
⟶
not
(
x0
x6
x11
)
⟶
not
(
x0
x7
x11
)
⟶
x0
x8
x11
⟶
not
(
x0
x9
x11
)
⟶
not
(
x0
x10
x11
)
⟶
x12
)
⟶
x12
Param
788a1..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Definition
e1ecf..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 .
∀ x12 : ο .
(
788a1..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
⟶
(
x1
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x2
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x3
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x4
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x5
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x6
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x7
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x8
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x9
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x10
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
x0
x1
x11
⟶
x0
x2
x11
⟶
x0
x3
x11
⟶
not
(
x0
x4
x11
)
⟶
not
(
x0
x5
x11
)
⟶
not
(
x0
x6
x11
)
⟶
not
(
x0
x7
x11
)
⟶
x0
x8
x11
⟶
not
(
x0
x9
x11
)
⟶
not
(
x0
x10
x11
)
⟶
x12
)
⟶
x12
Param
c9658..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Definition
c6073..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 .
∀ x12 : ο .
(
c9658..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
⟶
(
x1
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x2
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x3
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x4
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x5
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x6
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x7
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x8
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x9
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
(
x10
=
x11
⟶
∀ x13 : ο .
x13
)
⟶
x0
x1
x11
⟶
x0
x2
x11
⟶
x0
x3
x11
⟶
not
(
x0
x4
x11
)
⟶
not
(
x0
x5
x11
)
⟶
not
(
x0
x6
x11
)
⟶
not
(
x0
x7
x11
)
⟶
x0
x8
x11
⟶
not
(
x0
x9
x11
)
⟶
not
(
x0
x10
x11
)
⟶
x12
)
⟶
x12