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Proofgold Asset
asset id
a392b9f85af82d83a21e04f2c53065ad3c25e8cec0c91126039e3d68efa1d8f7
asset hash
4de74c97bcad4d936c4117cd66b09f46d8d6cd20af338774e0b179265b5b2b3c
bday / block
35127
tx
e848c..
preasset
doc published by
PrPhD..
Definition
False
False
:=
∀ x0 : ο .
x0
Definition
not
not
:=
λ x0 : ο .
x0
⟶
False
Theorem
d6bc4..
:
∀ x0 :
ι → ο
.
∀ x1 :
ι →
ι → ο
.
∀ x2 .
∀ x3 :
ι → ι
.
∀ x4 :
ι →
ι → ο
.
∀ x5 .
∀ x6 :
ι →
ι → ο
.
∀ x7 :
ι →
ι → ι
.
∀ x8 x9 x10 .
∀ x11 x12 :
ι →
ι → ι
.
∀ x13 x14 :
ι →
ι → ο
.
∀ x15 :
ι → ο
.
∀ x16 x17 x18 x19 .
∀ x20 :
ι → ο
.
∀ x21 .
∀ x22 :
ι → ο
.
∀ x23 x24 .
∀ x25 :
ι →
ι → ι
.
∀ x26 :
ι →
ι →
ι → ο
.
∀ x27 :
ι →
ι → ι
.
∀ x28 :
ι → ι
.
∀ x29 x30 x31 :
ι → ο
.
∀ x32 x33 x34 x35 .
∀ x36 :
ι → ο
.
∀ x37 x38 x39 :
ι →
ι → ι
.
∀ x40 :
ι →
ι → ο
.
∀ x41 :
ι →
ι → ι
.
∀ x42 x43 .
∀ x44 :
ι → ο
.
∀ x45 x46 x47 .
∀ x48 :
ι → ο
.
∀ x49 x50 x51 .
∀ x52 :
ι →
ι → ο
.
∀ x53 :
ι → ι
.
∀ x54 :
ι → ο
.
∀ x55 x56 .
∀ x57 :
ι → ο
.
∀ x58 :
ι → ι
.
∀ x59 :
ι → ο
.
∀ x60 :
ι →
ι →
ι →
ι →
ι → ι
.
∀ x61 :
ι →
ι →
ι → ι
.
∀ x62 :
ι →
ι → ι
.
∀ x63 :
ι → ο
.
∀ x64 :
ι →
ι → ι
.
∀ x65 :
ι → ο
.
∀ x66 :
ι →
ι →
ι → ο
.
∀ x67 x68 .
∀ x69 :
ι → ι
.
∀ x70 .
∀ x71 x72 :
ι →
ι → ι
.
∀ x73 .
∀ x74 :
ι →
ι → ι
.
∀ x75 x76 x77 :
ι → ο
.
∀ x78 :
ι →
ι → ο
.
∀ x79 :
ι → ο
.
(
∀ x80 x81 .
x79
x81
⟶
x79
x80
⟶
(
x78
x81
x80
⟶
False
)
⟶
(
x77
x80
⟶
False
)
⟶
(
x76
x81
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x0
x81
⟶
(
x81
=
x80
⟶
False
)
⟶
x0
x80
⟶
False
)
⟶
(
∀ x80 x81 .
x79
x81
⟶
x79
x80
⟶
(
x78
x81
x80
⟶
False
)
⟶
(
x76
x81
⟶
False
)
⟶
(
x77
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x1
x80
x81
⟶
x0
x81
⟶
False
)
⟶
(
∀ x80 x81 .
x79
x81
⟶
x79
x80
⟶
x78
x81
x80
⟶
(
x0
x81
⟶
False
)
⟶
(
x76
x80
⟶
False
)
⟶
(
x77
x81
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x0
x80
⟶
(
x80
=
x2
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x75
x80
⟶
(
x74
x80
x73
=
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 x82 .
x1
x80
x81
⟶
x4
x81
(
x3
x82
)
⟶
x0
x82
⟶
False
)
⟶
(
∀ x80 x81 .
x79
x81
⟶
x79
x80
⟶
x78
x81
x80
⟶
(
x0
x80
⟶
False
)
⟶
(
x77
x81
⟶
False
)
⟶
(
x76
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x75
x80
⟶
(
x74
x5
x80
=
x5
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 x82 .
x1
x81
x82
⟶
x4
x82
(
x3
x80
)
⟶
(
x4
x81
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x79
x81
⟶
x79
x80
⟶
x78
x81
x80
⟶
(
x76
x80
⟶
False
)
⟶
x76
x81
⟶
False
)
⟶
(
∀ x80 .
x75
x80
⟶
(
x72
x80
x5
=
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x6
x81
x80
⟶
(
x4
x81
(
x3
x80
)
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x4
x81
(
x3
x80
)
⟶
(
x6
x81
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x79
x81
⟶
x79
x80
⟶
x78
x81
x80
⟶
(
x77
x81
⟶
False
)
⟶
x77
x80
⟶
False
)
⟶
(
∀ x80 .
x75
x80
⟶
(
x71
x73
x80
=
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x4
x80
x81
⟶
(
x0
x81
⟶
False
)
⟶
(
x1
x80
x81
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x79
x81
⟶
x79
x80
⟶
x78
x81
x80
⟶
x77
x80
⟶
(
x77
x81
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x75
x80
⟶
(
x71
x80
x5
=
x5
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x1
x81
x80
⟶
(
x4
x81
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x79
x81
⟶
x79
x80
⟶
x78
x81
x80
⟶
x76
x81
⟶
(
x76
x80
⟶
False
)
⟶
False
)
⟶
(
(
x4
x2
x70
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x75
x80
⟶
(
x7
x80
x5
=
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x75
x81
⟶
x75
x80
⟶
(
x72
(
x69
x81
)
(
x69
x80
)
=
x72
x80
x81
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x75
x81
⟶
x75
x80
⟶
(
x7
(
x69
x81
)
(
x69
x80
)
=
x69
(
x7
x81
x80
)
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 x82 .
x75
x82
⟶
x75
x80
⟶
x75
x81
⟶
(
x71
(
x71
x82
x80
)
x81
=
x71
x82
(
x71
x80
x81
)
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 x82 .
x75
x82
⟶
x75
x80
⟶
x75
x81
⟶
(
x7
(
x7
x82
x80
)
x81
=
x7
x82
(
x7
x80
x81
)
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 x82 .
x75
x82
⟶
x75
x80
⟶
x75
x81
⟶
(
x71
(
x7
x82
x80
)
x81
=
x7
(
x71
x82
x81
)
(
x71
x80
x81
)
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 x82 .
x75
x82
⟶
x75
x80
⟶
x75
x81
⟶
(
x71
x82
(
x74
x80
x81
)
=
x74
(
x71
x82
x80
)
x81
⟶
False
)
⟶
False
)
⟶
(
(
x4
x67
x68
⟶
False
)
⟶
False
)
⟶
(
(
x4
x67
x8
⟶
False
)
⟶
False
)
⟶
(
(
x66
x67
x68
x8
⟶
False
)
⟶
False
)
⟶
(
(
x76
x67
⟶
False
)
⟶
False
)
⟶
(
x0
x67
⟶
False
)
⟶
(
(
x4
x9
x68
⟶
False
)
⟶
False
)
⟶
(
(
x4
x9
x8
⟶
False
)
⟶
False
)
⟶
(
(
x66
x9
x68
x8
⟶
False
)
⟶
False
)
⟶
(
(
x76
x9
⟶
False
)
⟶
False
)
⟶
(
x0
x9
⟶
False
)
⟶
(
∀ x80 .
x75
x80
⟶
(
x71
x80
(
x69
x73
)
=
x69
x80
⟶
False
)
⟶
False
)
⟶
(
(
x4
x73
x68
⟶
False
)
⟶
False
)
⟶
(
(
x4
x73
x8
⟶
False
)
⟶
False
)
⟶
(
(
x66
x73
x68
x8
⟶
False
)
⟶
False
)
⟶
(
(
x76
x73
⟶
False
)
⟶
False
)
⟶
(
x0
x73
⟶
False
)
⟶
(
∀ x80 x81 .
x75
x81
⟶
x75
x80
⟶
(
x7
x81
(
x69
x80
)
=
x72
x81
x80
⟶
False
)
⟶
False
)
⟶
(
(
x4
x10
x68
⟶
False
)
⟶
False
)
⟶
(
(
x4
x10
x8
⟶
False
)
⟶
False
)
⟶
(
(
x66
x10
x68
x8
⟶
False
)
⟶
False
)
⟶
(
(
x0
x10
⟶
False
)
⟶
False
)
⟶
(
(
x69
(
x74
(
x69
x67
)
x9
)
=
x74
x67
x9
⟶
False
)
⟶
False
)
⟶
(
(
x69
(
x74
(
x69
x9
)
x67
)
=
x74
x9
x67
⟶
False
)
⟶
False
)
⟶
(
(
x69
(
x74
(
x69
x73
)
x67
)
=
x74
x73
x67
⟶
False
)
⟶
False
)
⟶
(
(
x69
(
x74
(
x69
x73
)
x9
)
=
x74
x73
x9
⟶
False
)
⟶
False
)
⟶
(
(
x69
(
x74
x67
x9
)
=
x74
(
x69
x67
)
x9
⟶
False
)
⟶
False
)
⟶
(
(
x69
(
x74
x9
x67
)
=
x74
(
x69
x9
)
x67
⟶
False
)
⟶
False
)
⟶
(
(
x69
(
x74
x73
x67
)
=
x74
(
x69
x73
)
x67
⟶
False
)
⟶
False
)
⟶
(
(
x69
(
x74
x73
x9
)
=
x74
(
x69
x73
)
x9
⟶
False
)
⟶
False
)
⟶
(
(
x69
(
x69
x67
)
=
x67
⟶
False
)
⟶
False
)
⟶
(
(
x69
(
x69
x9
)
=
x9
⟶
False
)
⟶
False
)
⟶
(
(
x69
(
x69
x73
)
=
x73
⟶
False
)
⟶
False
)
⟶
(
(
x69
x67
=
x69
x67
⟶
False
)
⟶
False
)
⟶
(
(
x69
x9
=
x69
x9
⟶
False
)
⟶
False
)
⟶
(
(
x69
x73
=
x69
x73
⟶
False
)
⟶
False
)
⟶
(
(
x69
x10
=
x10
⟶
False
)
⟶
False
)
⟶
(
(
x71
(
x74
(
x69
x67
)
x9
)
(
x74
(
x69
x9
)
x67
)
=
x73
⟶
False
)
⟶
False
)
⟶
(
(
x71
(
x74
(
x69
x67
)
x9
)
(
x74
(
x69
x73
)
x67
)
=
x74
x73
x9
⟶
False
)
⟶
False
)
⟶
(
(
x71
(
x74
(
x69
x67
)
x9
)
(
x74
x9
x67
)
=
x69
x73
⟶
False
)
⟶
False
)
⟶
(
(
x71
(
x74
(
x69
x67
)
x9
)
(
x74
x73
x67
)
=
x74
(
x69
x73
)
x9
⟶
False
)
⟶
False
)
⟶
(
(
x71
(
x74
(
x69
x67
)
x9
)
(
x69
x9
)
=
x67
⟶
False
)
⟶
False
)
⟶
(
(
x71
(
x74
(
x69
x67
)
x9
)
x9
=
x69
x67
⟶
False
)
⟶
False
)
⟶
(
(
x71
(
x74
(
x69
x67
)
x9
)
x73
=
x74
(
x69
x67
)
x9
⟶
False
)
⟶
False
)
⟶
(
(
x71
(
x74
(
x69
x9
)
x67
)
(
x74
(
x69
x67
)
x9
)
=
x73
⟶
False
)
⟶
False
)
⟶
(
(
x71
(
x74
(
x69
x9
)
x67
)
(
x74
(
x69
x73
)
x9
)
=
x74
x73
x67
⟶
False
)
⟶
False
)
⟶
(
(
x71
(
x74
(
x69
x9
)
x67
)
(
x74
x67
x9
)
=
x69
x73
⟶
False
)
⟶
False
)
⟶
(
(
x71
(
x74
(
x69
x9
)
x67
)
(
x74
x73
x9
)
=
x74
(
x69
x73
)
x67
⟶
False
)
⟶
False
)
⟶
(
(
x71
(
x74
(
x69
x9
)
x67
)
(
x69
x67
)
=
x9
⟶
False
)
⟶
False
)
⟶
(
(
x71
(
x74
(
x69
x9
)
x67
)
x67
=
x69
x9
⟶
False
)
⟶
False
)
⟶
(
(
x71
(
x74
(
x69
x9
)
x67
)
x73
=
x74
(
x69
x9
)
x67
⟶
False
)
⟶
False
)
⟶
(
(
x71
(
x74
(
x69
x73
)
x67
)
(
x74
(
x69
x67
)
x9
)
=
x74
x73
x9
⟶
False
)
⟶
False
)
⟶
(
(
x71
(
x74
(
x69
x73
)
x67
)
(
x74
x67
x9
)
=
x74
(
x69
x73
)
x9
⟶
False
)
⟶
False
)
⟶
(
(
x71
(
x74
(
x69
x73
)
x67
)
(
x69
x67
)
=
x73
⟶
False
)
⟶
False
)
⟶
(
(
x71
(
x74
(
x69
x73
)
x67
)
(
x69
x9
)
=
x74
x9
x67
⟶
False
)
⟶
False
)
⟶
(
(
x71
(
x74
(
x69
x73
)
x67
)
x67
=
x69
x73
⟶
False
)
⟶
False
)
⟶
(
(
x71
(
x74
(
x69
x73
)
x67
)
x9
=
x74
(
x69
x9
)
x67
⟶
False
)
⟶
False
)
⟶
(
(
x71
(
x74
(
x69
x73
)
x67
)
x73
=
x74
(
x69
x73
)
x67
⟶
False
)
⟶
False
)
⟶
(
(
x71
(
x74
(
x69
x73
)
x9
)
(
x74
x9
x67
)
=
x74
(
x69
x73
)
x67
⟶
False
)
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