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Proofgold Signed Transaction
vin
PrRz8..
/
2f0be..
PUKVK..
/
04ff8..
vout
PrRz8..
/
bcfcb..
17.60 bars
TMdaj..
/
1a893..
ownership of
3e831..
as prop with payaddr
PrCnV..
rights free controlledby
PrCnV..
upto 0
TMLTt..
/
34c7e..
ownership of
36830..
as prop with payaddr
PrCnV..
rights free controlledby
PrCnV..
upto 0
PUKha..
/
25f12..
doc published by
PrCnV..
Known
FalseE
FalseE
:
False
⟶
∀ x0 : ο .
x0
Known
2901c..
EmptyE
:
∀ x0 .
In
x0
0
⟶
False
Known
d0de4..
Empty_eq
:
∀ x0 .
(
∀ x1 .
nIn
x1
x0
)
⟶
x0
=
0
Known
9d2e6..
nIn_I2
:
∀ x0 x1 .
(
In
x0
x1
⟶
False
)
⟶
nIn
x0
x1
Known
2109a..
UnionE2
:
∀ x0 x1 .
In
x1
(
Union
x0
)
⟶
∀ x2 : ο .
(
∀ x3 .
In
x1
x3
⟶
In
x3
x0
⟶
x2
)
⟶
x2
Known
367e6..
SubqE
:
∀ x0 x1 .
Subq
x0
x1
⟶
∀ x2 .
In
x2
x0
⟶
In
x2
x1
Theorem
3e831..
:
∀ x0 .
Subq
x0
(
Union
0
)
⟶
∀ x1 .
In
x1
x0
⟶
and
(
∀ x2 .
not
(
exactly5
x0
)
⟶
∀ x3 : ο .
(
∀ x4 .
and
(
Subq
x4
x0
)
(
∀ x5 .
In
x5
0
⟶
not
(
ordinal
x2
)
)
⟶
x3
)
⟶
x3
)
(
∀ x2 : ο .
(
∀ x3 .
and
(
In
x3
x1
)
(
∃ x4 .
not
(
TransSet
x1
)
)
⟶
x2
)
⟶
x2
)
⟶
atleast4
x1
(proof)