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Proofgold Asset
asset id
d99a07cdb62842e67d84be51d9e51bceb82b60f984b643ed07b67eb728cf75aa
asset hash
f028a5366cf7ebfa707968ba62e618a1e51628c1edbc31354cfffb4fefdc574f
bday / block
35144
tx
66e8b..
preasset
doc published by
PrPhD..
Definition
False
False
:=
∀ x0 : ο .
x0
Definition
not
not
:=
λ x0 : ο .
x0
⟶
False
Theorem
d6ffc..
:
∀ x0 :
ι →
ι → ο
.
∀ x1 :
ι → ι
.
∀ x2 :
ι → ο
.
∀ x3 :
ι →
ι → ι
.
∀ x4 .
∀ x5 :
ι →
ι → ι
.
∀ x6 .
∀ x7 :
ι → ι
.
∀ x8 x9 .
∀ x10 x11 :
ι → ι
.
∀ x12 .
∀ x13 :
ι →
ι →
ι → ο
.
∀ x14 :
ι →
ι → ο
.
∀ x15 .
∀ x16 x17 :
ι →
ι → ι
.
∀ x18 x19 :
ι →
ι → ο
.
∀ x20 .
(
∀ x21 x22 .
x19
x22
x20
⟶
x19
x21
x20
⟶
x18
x22
x21
⟶
(
x17
x22
(
x16
x21
x22
)
=
x21
⟶
False
)
⟶
False
)
⟶
(
∀ x21 x22 .
x19
x22
x20
⟶
x19
x21
x20
⟶
x18
x22
x21
⟶
(
x19
(
x16
x21
x22
)
x20
⟶
False
)
⟶
False
)
⟶
(
∀ x21 x22 x23 .
x19
x23
x20
⟶
x19
x21
x20
⟶
x19
x22
x20
⟶
(
x17
x23
(
x17
x21
x22
)
=
x17
(
x17
x23
x21
)
x22
⟶
False
)
⟶
False
)
⟶
(
∀ x21 x22 x23 .
x0
x21
x22
⟶
x19
x22
(
x1
x23
)
⟶
x2
x23
⟶
False
)
⟶
(
∀ x21 x22 .
x19
x22
x20
⟶
x19
x21
x20
⟶
x17
x22
x21
=
x15
⟶
(
x22
=
x15
⟶
False
)
⟶
False
)
⟶
(
∀ x21 x22 x23 .
x0
x22
x23
⟶
x19
x23
(
x1
x21
)
⟶
(
x19
x22
x21
⟶
False
)
⟶
False
)
⟶
(
∀ x21 x22 .
x14
x22
x21
⟶
(
x19
x22
(
x1
x21
)
⟶
False
)
⟶
False
)
⟶
(
∀ x21 x22 .
x19
x22
(
x1
x21
)
⟶
(
x14
x22
x21
⟶
False
)
⟶
False
)
⟶
(
∀ x21 x22 .
x19
x21
x22
⟶
(
x2
x22
⟶
False
)
⟶
(
x0
x21
x22
⟶
False
)
⟶
False
)
⟶
(
∀ x21 x22 .
x0
x22
x21
⟶
(
x19
x22
x21
⟶
False
)
⟶
False
)
⟶
(
∀ x21 x22 .
x19
x22
x20
⟶
x19
x21
x20
⟶
x17
x22
x21
=
x21
⟶
(
x22
=
x15
⟶
False
)
⟶
False
)
⟶
(
∀ x21 .
(
x14
x21
x21
⟶
False
)
⟶
False
)
⟶
(
∀ x21 x22 x23 .
(
x2
x23
⟶
False
)
⟶
(
x2
x21
⟶
False
)
⟶
x19
x21
(
x1
x23
)
⟶
x19
x22
x21
⟶
(
x13
x22
x23
x21
⟶
False
)
⟶
False
)
⟶
(
∀ x21 x22 x23 .
(
x2
x23
⟶
False
)
⟶
(
x2
x21
⟶
False
)
⟶
x19
x21
(
x1
x23
)
⟶
x13
x22
x23
x21
⟶
(
x19
x22
x21
⟶
False
)
⟶
False
)
⟶
(
(
x15
=
x12
⟶
False
)
⟶
False
)
⟶
(
∀ x21 x22 .
(
x2
x22
⟶
False
)
⟶
(
x2
x21
⟶
False
)
⟶
x19
x21
(
x1
x22
)
⟶
(
x13
(
x3
x21
x22
)
x22
x21
⟶
False
)
⟶
False
)
⟶
(
∀ x21 .
(
x19
(
x11
x21
)
x21
⟶
False
)
⟶
False
)
⟶
(
∀ x21 x22 x23 .
(
x2
x23
⟶
False
)
⟶
(
x2
x21
⟶
False
)
⟶
x19
x21
(
x1
x23
)
⟶
x13
x22
x23
x21
⟶
(
x19
x22
x23
⟶
False
)
⟶
False
)
⟶
(
∀ x21 x22 .
x19
x22
x20
⟶
x19
x21
x20
⟶
(
x19
(
x17
x22
x21
)
x20
⟶
False
)
⟶
False
)
⟶
(
∀ x21 x22 .
x19
x22
x4
⟶
x19
x21
x4
⟶
(
x13
(
x5
x22
x21
)
(
x1
x6
)
x4
⟶
False
)
⟶
False
)
⟶
(
∀ x21 .
x19
x21
x4
⟶
(
x19
(
x10
x21
)
x20
⟶
False
)
⟶
False
)
⟶
(
∀ x21 .
x19
x21
x20
⟶
(
x13
(
x7
x21
)
(
x1
x6
)
x4
⟶
False
)
⟶
False
)
⟶
(
(
x19
x4
(
x1
(
x1
x6
)
)
⟶
False
)
⟶
False
)
⟶
(
(
x19
x15
x6
⟶
False
)
⟶
False
)
⟶
(
∀ x21 x22 .
x19
x22
x20
⟶
x19
x21
x20
⟶
(
x21
=
x15
⟶
False
)
⟶
(
x22
=
x15
⟶
False
)
⟶
(
x17
x22
x21
=
x10
(
x5
(
x7
x22
)
(
x7
x21
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x21 x22 .
x19
x22
x20
⟶
x19
x21
x20
⟶
x22
=
x15
⟶
(
x17
x22
x21
=
x21
⟶
False
)
⟶
False
)
⟶
(
∀ x21 x22 .
x19
x22
x20
⟶
x19
x21
x20
⟶
x21
=
x15
⟶
(
x17
x22
x21
=
x22
⟶
False
)
⟶
False
)
⟶
(
∀ x21 x22 .
x19
x22
x20
⟶
x19
x21
x20
⟶
(
x18
x22
x21
⟶
False
)
⟶
(
x18
x21
x22
⟶
False
)
⟶
False
)
⟶
(
∀ x21 x22 .
x19
x22
x20
⟶
x19
x21
x20
⟶
(
x17
x22
x21
=
x17
x21
x22
⟶
False
)
⟶
False
)
⟶
(
∀ x21 x22 .
x19
x22
x4
⟶
x19
x21
x4
⟶
(
x5
x22
x21
=
x5
x21
x22
⟶
False
)
⟶
False
)
⟶
(
∀ x21 x22 .
x0
x21
x22
⟶
x0
x22
x21
⟶
False
)
⟶
(
x8
=
x9
⟶
False
)
⟶
(
(
x18
x9
x8
⟶
False
)
⟶
False
)
⟶
(
(
x18
x8
x9
⟶
False
)
⟶
False
)
⟶
(
(
x19
x9
x20
⟶
False
)
⟶
False
)
⟶
(
(
x19
x8
x20
⟶
False
)
⟶
False
)
⟶
False
...