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Proofgold Asset
asset id
85c63a3daf536b22e24d458b6acd5b616b84bdd2a43dedb53d28c2c775b5eb45
asset hash
bb02862c67af0dba15d31913b369599fb786c242bdd2c186230ef4381d9070b0
bday / block
35129
tx
52c48..
preasset
doc published by
PrPhD..
Definition
False
False
:=
∀ x0 : ο .
x0
Definition
not
not
:=
λ x0 : ο .
x0
⟶
False
Theorem
bec91..
:
∀ x0 :
ι →
ι → ι
.
∀ x1 x2 .
∀ x3 :
ι →
ι → ο
.
∀ x4 :
ι → ι
.
∀ x5 :
ι →
ι → ο
.
∀ x6 x7 :
ι →
ι → ι
.
∀ x8 x9 .
∀ x10 :
ι →
ι →
ι → ο
.
∀ x11 .
∀ x12 :
ι → ο
.
∀ x13 :
ι → ι
.
∀ x14 :
ι → ο
.
∀ x15 x16 .
∀ x17 :
ι → ο
.
∀ x18 x19 .
∀ x20 :
ι → ο
.
∀ x21 x22 x23 x24 .
∀ x25 :
ι →
ι → ο
.
∀ x26 :
ι →
ι → ι
.
∀ x27 :
ι → ο
.
∀ x28 :
ι →
ι → ι
.
∀ x29 :
ι → ι
.
∀ x30 :
ι →
ι → ι
.
∀ x31 x32 x33 :
ι → ο
.
∀ x34 .
∀ x35 x36 x37 :
ι → ο
.
∀ x38 :
ι →
ι →
ι → ο
.
∀ x39 :
ι →
ι → ι
.
∀ x40 :
ι → ο
.
∀ x41 :
ι →
ι → ι
.
∀ x42 x43 :
ι → ο
.
∀ x44 .
∀ x45 :
ι → ο
.
∀ x46 .
∀ x47 :
ι →
ι → ο
.
∀ x48 x49 x50 x51 x52 x53 .
∀ x54 :
ι → ο
.
∀ x55 :
ι → ι
.
∀ x56 .
∀ x57 :
ι → ο
.
∀ x58 .
∀ x59 :
ι → ι
.
∀ x60 .
∀ x61 :
ι →
ι → ο
.
∀ x62 x63 .
∀ x64 :
ι → ο
.
∀ x65 :
ι →
ι → ι
.
∀ x66 :
ι → ι
.
∀ x67 x68 :
ι →
ι → ι
.
∀ x69 :
ι → ι
.
∀ x70 :
ι → ο
.
(
∀ x71 x72 .
x70
x72
⟶
x70
x71
⟶
(
x66
(
x65
x72
x71
)
=
x67
(
x68
(
x69
x72
)
(
x66
x71
)
)
(
x68
(
x69
x71
)
(
x66
x72
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x71 x72 .
x70
x72
⟶
x70
x71
⟶
(
x69
(
x65
x72
x71
)
=
x0
(
x68
(
x69
x72
)
(
x69
x71
)
)
(
x68
(
x66
x72
)
(
x66
x71
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x71 x72 .
x64
x72
⟶
(
x72
=
x71
⟶
False
)
⟶
x64
x71
⟶
False
)
⟶
(
(
x66
x1
=
x2
⟶
False
)
⟶
False
)
⟶
(
(
x69
x1
=
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x71 x72 .
x3
x71
x72
⟶
x64
x72
⟶
False
)
⟶
(
∀ x71 .
x64
x71
⟶
(
x71
=
x62
⟶
False
)
⟶
False
)
⟶
(
∀ x71 x72 x73 .
x3
x71
x72
⟶
x5
x72
(
x4
x73
)
⟶
x64
x73
⟶
False
)
⟶
(
∀ x71 x72 x73 .
x3
x72
x73
⟶
x5
x73
(
x4
x71
)
⟶
(
x5
x72
x71
⟶
False
)
⟶
False
)
⟶
(
∀ x71 .
x70
x71
⟶
(
x6
x71
x63
=
x71
⟶
False
)
⟶
False
)
⟶
(
∀ x71 x72 .
x61
x72
x71
⟶
(
x5
x72
(
x4
x71
)
⟶
False
)
⟶
False
)
⟶
(
∀ x71 x72 .
x5
x72
(
x4
x71
)
⟶
(
x61
x72
x71
⟶
False
)
⟶
False
)
⟶
(
∀ x71 .
x70
x71
⟶
(
x65
x2
x71
=
x71
⟶
False
)
⟶
False
)
⟶
(
∀ x71 x72 .
x5
x71
x72
⟶
(
x64
x72
⟶
False
)
⟶
(
x3
x71
x72
⟶
False
)
⟶
False
)
⟶
(
∀ x71 .
x70
x71
⟶
(
x65
x71
x63
=
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x71 x72 .
x3
x72
x71
⟶
(
x5
x72
x71
⟶
False
)
⟶
False
)
⟶
(
(
x5
x62
x60
⟶
False
)
⟶
False
)
⟶
(
∀ x71 .
x70
x71
⟶
(
x7
x71
x63
=
x71
⟶
False
)
⟶
False
)
⟶
(
∀ x71 x72 .
x70
x72
⟶
x70
x71
⟶
(
x6
(
x59
x72
)
(
x59
x71
)
=
x6
x71
x72
⟶
False
)
⟶
False
)
⟶
(
∀ x71 x72 .
x70
x72
⟶
x70
x71
⟶
(
x7
(
x59
x72
)
(
x59
x71
)
=
x59
(
x7
x72
x71
)
⟶
False
)
⟶
False
)
⟶
(
∀ x71 x72 x73 .
x70
x73
⟶
x70
x71
⟶
x70
x72
⟶
(
x65
(
x65
x73
x71
)
x72
=
x65
x73
(
x65
x71
x72
)
⟶
False
)
⟶
False
)
⟶
(
∀ x71 x72 x73 .
x70
x73
⟶
x70
x71
⟶
x70
x72
⟶
(
x7
(
x7
x73
x71
)
x72
=
x7
x73
(
x7
x71
x72
)
⟶
False
)
⟶
False
)
⟶
(
∀ x71 x72 x73 .
x70
x73
⟶
x70
x71
⟶
x70
x72
⟶
(
x65
(
x7
x73
x71
)
x72
=
x7
(
x65
x73
x72
)
(
x65
x71
x72
)
⟶
False
)
⟶
False
)
⟶
(
(
x5
x9
x8
⟶
False
)
⟶
False
)
⟶
(
(
x5
x9
x58
⟶
False
)
⟶
False
)
⟶
(
(
x10
x9
x8
x58
⟶
False
)
⟶
False
)
⟶
(
(
x57
x9
⟶
False
)
⟶
False
)
⟶
(
x64
x9
⟶
False
)
⟶
(
∀ x71 .
x70
x71
⟶
(
x65
x71
(
x59
x2
)
=
x59
x71
⟶
False
)
⟶
False
)
⟶
(
(
x5
x2
x8
⟶
False
)
⟶
False
)
⟶
(
(
x5
x2
x58
⟶
False
)
⟶
False
)
⟶
(
(
x10
x2
x8
x58
⟶
False
)
⟶
False
)
⟶
(
(
x57
x2
⟶
False
)
⟶
False
)
⟶
(
x64
x2
⟶
False
)
⟶
(
∀ x71 x72 .
x70
x72
⟶
x70
x71
⟶
(
x7
x72
(
x59
x71
)
=
x6
x72
x71
⟶
False
)
⟶
False
)
⟶
(
(
x5
x11
x8
⟶
False
)
⟶
False
)
⟶
(
(
x5
x11
x58
⟶
False
)
⟶
False
)
⟶
(
(
x10
x11
x8
x58
⟶
False
)
⟶
False
)
⟶
(
(
x64
x11
⟶
False
)
⟶
False
)
⟶
(
(
x59
(
x59
x9
)
=
x9
⟶
False
)
⟶
False
)
⟶
(
(
x59
(
x59
x2
)
=
x2
⟶
False
)
⟶
False
)
⟶
(
(
x59
x9
=
x59
x9
⟶
False
)
⟶
False
)
⟶
(
(
x59
x2
=
x59
x2
⟶
False
)
⟶
False
)
⟶
(
(
x59
x11
=
x11
⟶
False
)
⟶
False
)
⟶
(
(
x59
(
x7
(
x65
(
x59
x9
)
x56
)
(
x59
x9
)
)
=
x7
(
x65
x9
x56
)
x9
⟶
False
)
⟶
False
)
⟶
(
(
x59
(
x7
(
x65
(
x59
x9
)
x56
)
(
x59
x2
)
)
=
x7
(
x65
x9
x56
)
x2
⟶
False
)
⟶
False
)
⟶
(
(
x59
(
x7
(
x65
(
x59
x9
)
x56
)
x9
)
=
x7
(
x65
x9
x56
)
(
x59
x9
)
⟶
False
)
⟶
False
)
⟶
(
(
x59
(
x7
(
x65
(
x59
x9
)
x56
)
x2
)
=
x7
(
x65
x9
x56
)
(
x59
x2
)
⟶
False
)
⟶
False
)
⟶
(
(
x59
(
x65
(
x59
x9
)
x56
)
=
x65
x9
x56
⟶
False
)
⟶
False
)
⟶
(
(
x59
(
x7
(
x65
(
x59
x2
)
x56
)
(
x59
x2
)
)
=
x7
x56
x2
⟶
False
)
⟶
False
)
⟶
(
(
x59
(
x7
(
x65
(
x59
x2
)
x56
)
x2
)
=
x7
x56
(
x59
x2
)
⟶
False
)
⟶
False
)
⟶
(
(
x59
(
x65
(
x59
x2
)
x56
)
=
x56
⟶
False
)
⟶
False
)
⟶
(
(
x59
(
x7
(
x65
x9
x56
)
(
x59
x9
)
)
=
x7
(
x65
(
x59
x9
)
x56
)
x9
⟶
False
)
⟶
False
)
⟶
(
(
x59
(
x7
(
x65
x9
x56
)
x9
)
=
x7
(
x65
(
x59
x9
)
x56
)
(
x59
x9
)
⟶
False
)
⟶
False
)
⟶
(
(
x59
(
x7
(
x65
x9
x56
)
x2
)
=
x7
(
x65
(
x59
x9
)
x56
)
(
x59
x2
)
⟶
False
)
⟶
False
)
⟶
(
(
x59
(
x65
x9
x56
)
=
x65
(
x59
x9
)
x56
⟶
False
)
⟶
False
)
⟶
(
(
x59
(
x7
x56
(
x59
x2
)
)
=
x7
(
x65
(
x59
x2
)
x56
)
x2
⟶
False
)
⟶
False
)
⟶
(
(
x59
(
x7
x56
x2
)
=
x7
(
x65
(
x59
x2
)
x56
)
(
x59
x2
)
⟶
False
)
⟶
False
)
⟶
(
(
x59
x56
=
x65
(
x59
x2
)
x56
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x59
x9
)
x2
=
x59
x9
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x59
x9
)
x11
=
x11
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x59
x9
)
(
x65
(
x59
x2
)
x56
)
=
x65
x9
x56
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x59
x9
)
x56
=
x65
(
x59
x9
)
x56
⟶
False
)
⟶
False
)
⟶
(
(
x65
x9
x2
=
x9
⟶
False
)
⟶
False
)
⟶
(
(
x65
x9
x11
=
x11
⟶
False
)
⟶
False
)
⟶
(
(
x65
x9
(
x65
(
x59
x2
)
x56
)
=
x65
(
x59
x9
)
x56
⟶
False
)
⟶
False
)
⟶
(
(
x65
x9
x56
=
x65
x9
x56
⟶
False
)
⟶
False
)
⟶
(
(
x65
x2
(
x59
x9
)
=
x59
x9
⟶
False
)
⟶
False
)
⟶
(
(
x65
x2
x9
=
x9
⟶
False
)
⟶
False
)
⟶
(
(
x65
x2
x2
=
x2
⟶
False
)
⟶
False
)
⟶
(
(
x65
x2
x11
=
x11
⟶
False
)
⟶
False
)
⟶
(
(
x65
x2
(
x7
(
x65
(
x59
x2
)
x56
)
x2
)
=
x7
(
x65
(
x59
x2
)
x56
)
x2
⟶
False
)
⟶
False
)
⟶
(
(
x65
x2
(
x65
(
x59
x2
)
x56
)
=
x65
(
x59
x2
)
x56
⟶
False
)
⟶
False
)
⟶
(
(
x65
x2
(
x65
x9
x56
)
=
x65
x9
x56
⟶
False
)
⟶
False
)
⟶
(
(
x65
x2
x56
=
x56
⟶
False
)
⟶
False
)
⟶
(
(
x65
x11
(
x59
x9
)
=
x11
⟶
False
)
⟶
False
)
⟶
(
(
x65
x11
x9
=
x11
⟶
False
)
⟶
False
)
⟶
(
(
x65
x11
x2
=
x11
⟶
False
)
⟶
False
)
⟶
(
(
x65
x11
x11
=
x11
⟶
False
)
⟶
False
)
⟶
(
(
x65
x11
x56
=
x11
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x65
(
x59
x9
)
x56
)
x2
=
x65
(
x59
x9
)
x56
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x65
(
x59
x9
)
x56
)
(
x65
(
x59
x2
)
x56
)
=
x59
x9
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x65
(
x59
x9
)
x56
)
x56
=
x9
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x7
(
x65
(
x59
x2
)
x56
)
(
x59
x2
)
)
x2
=
x7
(
x65
(
x59
x2
)
x56
)
(
x59
x2
)
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x7
(
x65
(
x59
x2
)
x56
)
(
x59
x2
)
)
(
x65
(
x59
x2
)
x56
)
=
x7
x56
(
x59
x2
)
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x7
(
x65
(
x59
x2
)
x56
)
(
x59
x2
)
)
x56
=
x7
(
x65
(
x59
x2
)
x56
)
x2
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x7
(
x65
(
x59
x2
)
x56
)
x9
)
x2
=
x7
(
x65
(
x59
x2
)
x56
)
x9
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x7
(
x65
(
x59
x2
)
x56
)
x9
)
(
x65
(
x59
x2
)
x56
)
=
x7
(
x65
(
x59
x9
)
x56
)
(
x59
x2
)
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x7
(
x65
(
x59
x2
)
x56
)
x9
)
x56
=
x7
(
x65
x9
x56
)
x2
⟶
False
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x59
x2
)
x56
)
=
x65
(
x59
x2
)
x56
⟶
False
)
⟶
False
)
⟶
(
(
x6
(
x7
(
x65
(
x59
x2
)
x56
)
(
x59
x2
)
)
(
x59
x2
)
=
x65
(
x59
x2
)
x56
⟶
False
)
⟶
False
)
⟶
(
(
x6
(
x7
(
x65
(