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Proofgold Address
address
PURqB7sJEouZuCBqmsHV4CoXNPd7uFHmghV
total
0
mg
-
conjpub
-
current assets
1effa..
/
dc015..
bday:
18372
doc published by
Pr4zB..
Param
ordsucc
ordsucc
:
ι
→
ι
Param
u19
:
ι
Definition
u20
:=
ordsucc
u19
Param
u1
:
ι
Param
u2
:
ι
Param
u3
:
ι
Param
u4
:
ι
Param
u5
:
ι
Param
u6
:
ι
Param
u7
:
ι
Param
u8
:
ι
Param
u9
:
ι
Param
u10
:
ι
Param
u11
:
ι
Param
u12
:
ι
Param
u13
:
ι
Param
u14
:
ι
Param
u15
:
ι
Param
u16
:
ι
Param
u17
:
ι
Param
u18
:
ι
Definition
or
or
:=
λ x0 x1 : ο .
∀ x2 : ο .
(
x0
⟶
x2
)
⟶
(
x1
⟶
x2
)
⟶
x2
Known
ordsuccE
ordsuccE
:
∀ x0 x1 .
x1
∈
ordsucc
x0
⟶
or
(
x1
∈
x0
)
(
x1
=
x0
)
Known
27a71..
:
∀ x0 .
x0
∈
u19
⟶
∀ x1 :
ι → ο
.
x1
0
⟶
x1
u1
⟶
x1
u2
⟶
x1
u3
⟶
x1
u4
⟶
x1
u5
⟶
x1
u6
⟶
x1
u7
⟶
x1
u8
⟶
x1
u9
⟶
x1
u10
⟶
x1
u11
⟶
x1
u12
⟶
x1
u13
⟶
x1
u14
⟶
x1
u15
⟶
x1
u16
⟶
x1
u17
⟶
x1
u18
⟶
x1
x0
Theorem
6ab99..
:
∀ x0 .
x0
∈
u20
⟶
∀ x1 :
ι → ο
.
x1
0
⟶
x1
u1
⟶
x1
u2
⟶
x1
u3
⟶
x1
u4
⟶
x1
u5
⟶
x1
u6
⟶
x1
u7
⟶
x1
u8
⟶
x1
u9
⟶
x1
u10
⟶
x1
u11
⟶
x1
u12
⟶
x1
u13
⟶
x1
u14
⟶
x1
u15
⟶
x1
u16
⟶
x1
u17
⟶
x1
u18
⟶
x1
u19
⟶
x1
x0
(proof)
Definition
u21
:=
ordsucc
u20
Theorem
a039e..
:
∀ x0 .
x0
∈
u21
⟶
∀ x1 :
ι → ο
.
x1
0
⟶
x1
u1
⟶
x1
u2
⟶
x1
u3
⟶
x1
u4
⟶
x1
u5
⟶
x1
u6
⟶
x1
u7
⟶
x1
u8
⟶
x1
u9
⟶
x1
u10
⟶
x1
u11
⟶
x1
u12
⟶
x1
u13
⟶
x1
u14
⟶
x1
u15
⟶
x1
u16
⟶
x1
u17
⟶
x1
u18
⟶
x1
u19
⟶
x1
u20
⟶
x1
x0
(proof)
Definition
u22
:=
ordsucc
u21
Theorem
df354..
:
∀ x0 .
x0
∈
u22
⟶
∀ x1 :
ι → ο
.
x1
0
⟶
x1
u1
⟶
x1
u2
⟶
x1
u3
⟶
x1
u4
⟶
x1
u5
⟶
x1
u6
⟶
x1
u7
⟶
x1
u8
⟶
x1
u9
⟶
x1
u10
⟶
x1
u11
⟶
x1
u12
⟶
x1
u13
⟶
x1
u14
⟶
x1
u15
⟶
x1
u16
⟶
x1
u17
⟶
x1
u18
⟶
x1
u19
⟶
x1
u20
⟶
x1
u21
⟶
x1
x0
(proof)
Definition
u23
:=
ordsucc
u22
Theorem
eae4d..
:
∀ x0 .
x0
∈
u23
⟶
∀ x1 :
ι → ο
.
x1
0
⟶
x1
u1
⟶
x1
u2
⟶
x1
u3
⟶
x1
u4
⟶
x1
u5
⟶
x1
u6
⟶
x1
u7
⟶
x1
u8
⟶
x1
u9
⟶
x1
u10
⟶
x1
u11
⟶
x1
u12
⟶
x1
u13
⟶
x1
u14
⟶
x1
u15
⟶
x1
u16
⟶
x1
u17
⟶
x1
u18
⟶
x1
u19
⟶
x1
u20
⟶
x1
u21
⟶
x1
u22
⟶
x1
x0
(proof)
Definition
u24
:=
ordsucc
u23
Theorem
adedd..
:
∀ x0 .
x0
∈
u24
⟶
∀ x1 :
ι → ο
.
x1
0
⟶
x1
u1
⟶
x1
u2
⟶
x1
u3
⟶
x1
u4
⟶
x1
u5
⟶
x1
u6
⟶
x1
u7
⟶
x1
u8
⟶
x1
u9
⟶
x1
u10
⟶
x1
u11
⟶
x1
u12
⟶
x1
u13
⟶
x1
u14
⟶
x1
u15
⟶
x1
u16
⟶
x1
u17
⟶
x1
u18
⟶
x1
u19
⟶
x1
u20
⟶
x1
u21
⟶
x1
u22
⟶
x1
u23
⟶
x1
x0
(proof)
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