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Proofgold Asset
asset id
041ce3e4d5f6d3c4248b7dbdc0258c9d93d69856273e8265d98f3de9d9f06523
asset hash
a2cef7821d905ce05094db0a4c3adaca5e2610e03f3a31c2d41aec1718e853dd
bday / block
48183
tx
4822d..
preasset
doc published by
PrGM6..
Definition
False
False
:=
∀ x0 : ο .
x0
Definition
not
not
:=
λ x0 : ο .
x0
⟶
False
Definition
2f869..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 .
∀ x5 : ο .
(
(
x1
=
x2
⟶
∀ x6 : ο .
x6
)
⟶
(
x1
=
x3
⟶
∀ x6 : ο .
x6
)
⟶
(
x2
=
x3
⟶
∀ x6 : ο .
x6
)
⟶
(
x1
=
x4
⟶
∀ x6 : ο .
x6
)
⟶
(
x2
=
x4
⟶
∀ x6 : ο .
x6
)
⟶
(
x3
=
x4
⟶
∀ x6 : ο .
x6
)
⟶
not
(
x0
x1
x2
)
⟶
not
(
x0
x1
x3
)
⟶
not
(
x0
x2
x3
)
⟶
not
(
x0
x1
x4
)
⟶
not
(
x0
x2
x4
)
⟶
x0
x3
x4
⟶
x5
)
⟶
x5
Definition
87c36..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 .
∀ x6 : ο .
(
2f869..
x0
x1
x2
x3
x4
⟶
(
x1
=
x5
⟶
∀ x7 : ο .
x7
)
⟶
(
x2
=
x5
⟶
∀ x7 : ο .
x7
)
⟶
(
x3
=
x5
⟶
∀ x7 : ο .
x7
)
⟶
(
x4
=
x5
⟶
∀ x7 : ο .
x7
)
⟶
not
(
x0
x1
x5
)
⟶
x0
x2
x5
⟶
not
(
x0
x3
x5
)
⟶
x0
x4
x5
⟶
x6
)
⟶
x6
Definition
f201d..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 .
∀ x7 : ο .
(
87c36..
x0
x1
x2
x3
x4
x5
⟶
(
x1
=
x6
⟶
∀ x8 : ο .
x8
)
⟶
(
x2
=
x6
⟶
∀ x8 : ο .
x8
)
⟶
(
x3
=
x6
⟶
∀ x8 : ο .
x8
)
⟶
(
x4
=
x6
⟶
∀ x8 : ο .
x8
)
⟶
(
x5
=
x6
⟶
∀ x8 : ο .
x8
)
⟶
x0
x1
x6
⟶
not
(
x0
x2
x6
)
⟶
x0
x3
x6
⟶
not
(
x0
x4
x6
)
⟶
x0
x5
x6
⟶
x7
)
⟶
x7
Definition
6648a..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 .
∀ x7 : ο .
(
87c36..
x0
x1
x2
x3
x4
x5
⟶
(
x1
=
x6
⟶
∀ x8 : ο .
x8
)
⟶
(
x2
=
x6
⟶
∀ x8 : ο .
x8
)
⟶
(
x3
=
x6
⟶
∀ x8 : ο .
x8
)
⟶
(
x4
=
x6
⟶
∀ x8 : ο .
x8
)
⟶
(
x5
=
x6
⟶
∀ x8 : ο .
x8
)
⟶
not
(
x0
x1
x6
)
⟶
x0
x2
x6
⟶
x0
x3
x6
⟶
not
(
x0
x4
x6
)
⟶
not
(
x0
x5
x6
)
⟶
x7
)
⟶
x7
Definition
836ee..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 .
∀ x8 : ο .
(
6648a..
x0
x1
x2
x3
x4
x5
x6
⟶
(
x1
=
x7
⟶
∀ x9 : ο .
x9
)
⟶
(
x2
=
x7
⟶
∀ x9 : ο .
x9
)
⟶
(
x3
=
x7
⟶
∀ x9 : ο .
x9
)
⟶
(
x4
=
x7
⟶
∀ x9 : ο .
x9
)
⟶
(
x5
=
x7
⟶
∀ x9 : ο .
x9
)
⟶
(
x6
=
x7
⟶
∀ x9 : ο .
x9
)
⟶
x0
x1
x7
⟶
not
(
x0
x2
x7
)
⟶
not
(
x0
x3
x7
)
⟶
not
(
x0
x4
x7
)
⟶
x0
x5
x7
⟶
x0
x6
x7
⟶
x8
)
⟶
x8
Definition
89dbd..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 x7 x8 .
∀ x9 : ο .
(
836ee..
x0
x1
x2
x3
x4
x5
x6
x7
⟶
(
x1
=
x8
⟶
∀ x10 : ο .
x10
)
⟶
(
x2
=
x8
⟶
∀ x10 : ο .
x10
)
⟶
(
x3
=
x8
⟶
∀ x10 : ο .
x10
)
⟶
(
x4
=
x8
⟶
∀ x10 : ο .
x10
)
⟶
(
x5
=
x8
⟶
∀ x10 : ο .
x10
)
⟶
(
x6
=
x8
⟶
∀ x10 : ο .
x10
)
⟶
(
x7
=
x8
⟶
∀ x10 : ο .
x10
)
⟶
x0
x1
x8
⟶
x0
x2
x8
⟶
not
(
x0
x3
x8
)
⟶
not
(
x0
x4
x8
)
⟶
not
(
x0
x5
x8
)
⟶
not
(
x0
x6
x8
)
⟶
not
(
x0
x7
x8
)
⟶
x9
)
⟶
x9
Definition
Subq
Subq
:=
λ x0 x1 .
∀ x2 .
x2
∈
x0
⟶
x2
∈
x1
Param
atleastp
atleastp
:
ι
→
ι
→
ο
Definition
cdfa5..
:=
λ x0 x1 .
λ x2 :
ι →
ι → ο
.
∀ x3 .
x3
⊆
x1
⟶
atleastp
x0
x3
⟶
not
(
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
(
x4
=
x5
⟶
∀ x6 : ο .
x6
)
⟶
x2
x4
x5
)
Param
u4
:
ι
Definition
86706..
:=
cdfa5..
u4
Definition
35fb6..
:=
λ x0 .
λ x1 :
ι →
ι → ο
.
86706..
x0
(
λ x2 x3 .
not
(
x1
x2
x3
)
)
Param
SetAdjoin
SetAdjoin
:
ι
→
ι
→
ι
Param
UPair
UPair
:
ι
→
ι
→
ι
Definition
or
or
:=
λ x0 x1 : ο .
∀ x2 : ο .
(
x0
⟶
x2
)
⟶
(
x1
⟶
x2
)
⟶
x2
Known
xm
xm
:
∀ x0 : ο .
or
x0
(
not
x0
)
Known
dneg
dneg
:
∀ x0 : ο .
not
(
not
x0
)
⟶
x0
Param
equip
equip
:
ι
→
ι
→
ο
Known
equip_atleastp
equip_atleastp
:
∀ x0 x1 .
equip
x0
x1
⟶
atleastp
x0
x1
Known
7204a..
:
∀ x0 x1 x2 x3 .
(
x0
=
x1
⟶
∀ x4 : ο .
x4
)
⟶
(
x0
=
x2
⟶
∀ x4 : ο .
x4
)
⟶
(
x1
=
x2
⟶
∀ x4 : ο .
x4
)
⟶
(
x0
=
x3
⟶
∀ x4 : ο .
x4
)
⟶
(
x1
=
x3
⟶
∀ x4 : ο .
x4
)
⟶
(
x2
=
x3
⟶
∀ x4 : ο .
x4
)
⟶
equip
u4
(
SetAdjoin
(
SetAdjoin
(
UPair
x0
x1
)
x2
)
x3
)
Known
58c12..
:
∀ x0 :
ι →
ι → ο
.
∀ x1 x2 x3 x4 .
x0
x1
x2
⟶
x0
x1
x3
⟶
x0
x1
x4
⟶
x0
x2
x3
⟶
x0
x2
x4
⟶
x0
x3
x4
⟶
(
∀ x5 .
x5
∈
SetAdjoin
(
SetAdjoin
(
UPair
x1
x2
)
x3
)
x4
⟶
∀ x6 .
x6
∈
SetAdjoin
(
SetAdjoin
(
UPair
x1
x2
)
x3
)
x4
⟶
x0
x5
x6
⟶
x0
x6
x5
)
⟶
∀ x5 .
x5
∈
SetAdjoin
(
SetAdjoin
(
UPair
x1
x2
)
x3
)
x4
⟶
∀ x6 .
x6
∈
SetAdjoin
(
SetAdjoin
(
UPair
x1
x2
)
x3
)
x4
⟶
(
x5
=
x6
⟶
∀ x7 : ο .
x7
)
⟶
x0
x5
x6
Known
c88f0..
:
∀ x0 x1 .
x1
∈
x0
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
SetAdjoin
(
SetAdjoin
(
UPair
x1
x2
)
x3
)
x4
⊆
x0
Theorem
d9eaf..
:
∀ x0 :
ι →
ι → ο
.
∀ x1 x2 .
x2
∈
x1
⟶
∀ x3 .
x3
∈
x1
⟶
∀ x4 .
x4
∈
x1
⟶
∀ x5 .
x5
∈
x1
⟶
∀ x6 .
x6
∈
x1
⟶
∀ x7 .
x7
∈
x1
⟶
∀ x8 .
x8
∈
x1
⟶
∀ x9 .
x9
∈
x1
⟶
∀ x10 .
x10
∈
x1
⟶
∀ x11 .
x11
∈
x1
⟶
∀ x12 .
x12
∈
x1
⟶
∀ x13 .
x13
∈
x1
⟶
∀ x14 .
x14
∈
x1
⟶
∀ x15 .
x15
∈
x1
⟶
(
∀ x16 .
x16
∈
x1
⟶
∀ x17 .
x17
∈
x1
⟶
x0
x16
x17
⟶
x0
x17
x16
)
⟶
(
x2
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
f201d..
x0
x2
x3
x4
x5
x6
x7
⟶
89dbd..
(
λ x16 x17 .
not
(
x0
x16
x17
)
)
x8
x9
x10
x11
x12
x13
x14
x15
⟶
86706..
x1
x0
⟶
35fb6..
x1
x0
⟶
(
x0
x2
x8
⟶
not
(
x0
x2
x10
)
⟶
False
)
⟶
(
x0
x2
x8
⟶
not
(
x0
x2
x11
)
⟶
False
)
⟶
(
x0
x2
x8
⟶
not
(
x0
x2
x15
)
⟶
False
)
⟶
(
x0
x2
x8
⟶
x0
x3
x15
⟶
not
(
x0
x3
x11
)
⟶
False
)
⟶
False
...
Known
6f045..
:
∀ 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
⟶
89dbd..
x1
x2
x3
x4
x5
x6
x7
x8
x9
⟶
89dbd..
x1
x9
x8
x5
x4
x7
x6
x3
x2
Theorem
7e0df..
:
∀ x0 :
ι →
ι → ο
.
∀ x1 x2 .
x2
∈
x1
⟶
∀ x3 .
x3
∈
x1
⟶
∀ x4 .
x4
∈
x1
⟶
∀ x5 .
x5
∈
x1
⟶
∀ x6 .
x6
∈
x1
⟶
∀ x7 .
x7
∈
x1
⟶
∀ x8 .
x8
∈
x1
⟶
∀ x9 .
x9
∈
x1
⟶
∀ x10 .
x10
∈
x1
⟶
∀ x11 .
x11
∈
x1
⟶
∀ x12 .
x12
∈
x1
⟶
∀ x13 .
x13
∈
x1
⟶
∀ x14 .
x14
∈
x1
⟶
∀ x15 .
x15
∈
x1
⟶
(
∀ x16 .
x16
∈
x1
⟶
∀ x17 .
x17
∈
x1
⟶
x0
x16
x17
⟶
x0
x17
x16
)
⟶
(
x2
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
f201d..
x0
x2
x3
x4
x5
x6
x7
⟶
89dbd..
(
λ x16 x17 .
not
(
x0
x16
x17
)
)
x8
x9
x10
x11
x12
x13
x14
x15
⟶
86706..
x1
x0
⟶
35fb6..
x1
x0
⟶
(
x0
x2
x15
⟶
not
(
x0
x2
x11
)
⟶
False
)
⟶
(
x0
x2
x15
⟶
not
(
x0
x2
x10
)
⟶
False
)
⟶
(
x0
x2
x15
⟶
x0
x3
x8
⟶
not
(
x0
x3
x10
)
⟶
False
)
⟶
False
...
Known
a4071..
:
∀ 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
⟶
89dbd..
x1
x2
x3
x4
x5
x6
x7
x8
x9
⟶
89dbd..
x1
x2
x3
x5
x4
x7
x6
x8
x9
Known
3cb06..
:
∀ 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
⟶
89dbd..
x1
x2
x3
x4
x5
x6
x7
x8
x9
⟶
89dbd..
x1
x4
x6
x2
x9
x3
x8
x7
x5
Theorem
bc193..
:
∀ 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
⟶
89dbd..
x1
x2
x3
x4
x5
x6
x7
x8
x9
⟶
89dbd..
x1
x4
x6
x9
x2
x8
x3
x7
x5
...
Theorem
fee2d..
:
∀ x0 :
ι →
ι → ο
.
∀ x1 x2 .
x2
∈
x1
⟶
∀ x3 .
x3
∈
x1
⟶
∀ x4 .
x4
∈
x1
⟶
∀ x5 .
x5
∈
x1
⟶
∀ x6 .
x6
∈
x1
⟶
∀ x7 .
x7
∈
x1
⟶
∀ x8 .
x8
∈
x1
⟶
∀ x9 .
x9
∈
x1
⟶
∀ x10 .
x10
∈
x1
⟶
∀ x11 .
x11
∈
x1
⟶
∀ x12 .
x12
∈
x1
⟶
∀ x13 .
x13
∈
x1
⟶
∀ x14 .
x14
∈
x1
⟶
∀ x15 .
x15
∈
x1
⟶
(
∀ x16 .
x16
∈
x1
⟶
∀ x17 .
x17
∈
x1
⟶
x0
x16
x17
⟶
x0
x17
x16
)
⟶
(
x2
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
f201d..
x0
x2
x3
x4
x5
x6
x7
⟶
89dbd..
(
λ x16 x17 .
not
(
x0
x16
x17
)
)
x8
x9
x10
x11
x12
x13
x14
x15
⟶
86706..
x1
x0
⟶
35fb6..
x1
x0
⟶
(
x0
x2
x11
⟶
x0
x3
x10
⟶
not
(
x0
x3
x15
)
⟶
False
)
⟶
(
x0
x2
x11
⟶
not
(
x0
x2
x8
)
⟶
False
)
⟶
False
...
Known
99aa6..
:
∀ 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
⟶
f201d..
x1
x2
x3
x4
x5
x6
x7
⟶
f201d..
x1
x3
x2
x5
x4
x7
x6
Theorem
c551f..
:
∀ x0 :
ι →
ι → ο
.
∀ x1 x2 .
x2
∈
x1
⟶
∀ x3 .
x3
∈
x1
⟶
∀ x4 .
x4
∈
x1
⟶
∀ x5 .
x5
∈
x1
⟶
∀ x6 .
x6
∈
x1
⟶
∀ x7 .
x7
∈
x1
⟶
∀ x8 .
x8
∈
x1
⟶
∀ x9 .
x9
∈
x1
⟶
∀ x10 .
x10
∈
x1
⟶
∀ x11 .
x11
∈
x1
⟶
∀ x12 .
x12
∈
x1
⟶
∀ x13 .
x13
∈
x1
⟶
∀ x14 .
x14
∈
x1
⟶
∀ x15 .
x15
∈
x1
⟶
(
∀ x16 .
x16
∈
x1
⟶
∀ x17 .
x17
∈
x1
⟶
x0
x16
x17
⟶
x0
x17
x16
)
⟶
(
x2
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
f201d..
x0
x2
x3
x4
x5
x6
x7
⟶
89dbd..
(
λ x16 x17 .
not
(
x0
x16
x17
)
)
x8
x9
x10
x11
x12
x13
x14
x15
⟶
86706..
x1
x0
⟶
35fb6..
x1
x0
⟶
(
x0
x3
x15
⟶
not
(
x0
x3
x10
)
⟶
False
)
⟶
False
...
Known
e5dcb..
:
∀ 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
⟶
89dbd..
x1
x2
x3
x4
x5
x6
x7
x8
x9
⟶
89dbd..
x1
x9
x8
x4
x5
x6
x7
x3
x2
Theorem
2cb02..
:
∀ x0 :
ι →
ι → ο
.
∀ x1 x2 .
x2
∈
x1
⟶
∀ x3 .
x3
∈
x1
⟶
∀ x4 .
x4
∈
x1
⟶
∀ x5 .
x5
∈
x1
⟶
∀ x6 .
x6
∈
x1
⟶
∀ x7 .
x7
∈
x1
⟶
∀ x8 .
x8
∈
x1
⟶
∀ x9 .
x9
∈
x1
⟶
∀ x10 .
x10
∈
x1
⟶
∀ x11 .
x11
∈
x1
⟶
∀ x12 .
x12
∈
x1
⟶
∀ x13 .
x13
∈
x1
⟶
∀ x14 .
x14
∈
x1
⟶
∀ x15 .
x15
∈
x1
⟶
(
∀ x16 .
x16
∈
x1
⟶
∀ x17 .
x17
∈
x1
⟶
x0
x16
x17
⟶
x0
x17
x16
)
⟶
(
x2
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
f201d..
x0
x2
x3
x4
x5
x6
x7
⟶
89dbd..
(
λ x16 x17 .
not
(
x0
x16
x17
)
)
x8
x9
x10
x11
x12
x13
x14
x15
⟶
86706..
x1
x0
⟶
35fb6..
x1
x0
⟶
(
x0
x2
x8
⟶
not
(
x0
x2
x10
)
⟶
False
)
⟶
False
...
Known
eab56..
:
∀ 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
⟶
89dbd..
x1
x2
x3
x4
x5
x6
x7
x8
x9
⟶
89dbd..
x1
x5
x7
x2
x9
x3
x8
x6
x4
Theorem
43b05..
:
∀ x0 :
ι →
ι → ο
.
∀ x1 x2 .
x2
∈
x1
⟶
∀ x3 .
x3
∈
x1
⟶
∀ x4 .
x4
∈
x1
⟶
∀ x5 .
x5
∈
x1
⟶
∀ x6 .
x6
∈
x1
⟶
∀ x7 .
x7
∈
x1
⟶
∀ x8 .
x8
∈
x1
⟶
∀ x9 .
x9
∈
x1
⟶
∀ x10 .
x10
∈
x1
⟶
∀ x11 .
x11
∈
x1
⟶
∀ x12 .
x12
∈
x1
⟶
∀ x13 .
x13
∈
x1
⟶
∀ x14 .
x14
∈
x1
⟶
∀ x15 .
x15
∈
x1
⟶
(
∀ x16 .
x16
∈
x1
⟶
∀ x17 .
x17
∈
x1
⟶
x0
x16
x17
⟶
x0
x17
x16
)
⟶
(
x2
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
f201d..
x0
x2
x3
x4
x5
x6
x7
⟶
89dbd..
(
λ x16 x17 .
not
(
x0
x16
x17
)
)
x8
x9
x10
x11
x12
x13
x14
x15
⟶
86706..
x1
x0
⟶
35fb6..
x1
x0
⟶
False
...