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Proofgold Asset
asset id
eb302c0f47365433642199320f5009a4c28bb70b9c7bbef8a28a2a9ae5716d26
asset hash
a422bd49946735b08ee0b6235d28075b8ae09cfaf46cabafae4b49c682854fde
bday / block
34769
tx
a7dc9..
preasset
doc published by
Pr4zB..
Param
0314a..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
not
not
:
ο
→
ο
Definition
f5da9..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 .
∀ x10 : ο .
(
0314a..
x0
x1
x2
x3
x4
x5
x6
x7
x8
⟶
(
x1
=
x9
⟶
∀ x11 : ο .
x11
)
⟶
(
x2
=
x9
⟶
∀ x11 : ο .
x11
)
⟶
(
x3
=
x9
⟶
∀ x11 : ο .
x11
)
⟶
(
x4
=
x9
⟶
∀ x11 : ο .
x11
)
⟶
(
x5
=
x9
⟶
∀ x11 : ο .
x11
)
⟶
(
x6
=
x9
⟶
∀ x11 : ο .
x11
)
⟶
(
x7
=
x9
⟶
∀ x11 : ο .
x11
)
⟶
(
x8
=
x9
⟶
∀ x11 : ο .
x11
)
⟶
not
(
x0
x1
x9
)
⟶
not
(
x0
x2
x9
)
⟶
x0
x3
x9
⟶
not
(
x0
x4
x9
)
⟶
not
(
x0
x5
x9
)
⟶
x0
x6
x9
⟶
not
(
x0
x7
x9
)
⟶
x0
x8
x9
⟶
x10
)
⟶
x10
Known
1b5c5..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
0314a..
x1
x2
x3
x4
x5
x6
x7
x8
x9
⟶
0314a..
x1
x3
x2
x4
x5
x6
x9
x8
x7
Theorem
abf2c..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
f5da9..
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
⟶
f5da9..
x1
x3
x2
x4
x5
x6
x9
x8
x7
x10
(proof)