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Proofgold Asset
asset id
ccc2608059cffc39cf4a6f68554ff44629991bb20d8990ac6b1c2e055cb599ee
asset hash
7ce3112a5da05fcfe9f91b832510032e8850b2694da17b9138e8f4c15fa45de9
bday / block
3231
tx
65ec3..
preasset
doc published by
PrJJf..
Known
Eps_i_ex
Eps_i_R2
:
∀ x0 :
ι → ο
.
(
∀ x1 : ο .
(
∀ x2 .
x0
x2
⟶
x1
)
⟶
x1
)
⟶
x0
(
Eps_i
x0
)
Known
39854..
andEL
:
∀ x0 x1 : ο .
and
x0
x1
⟶
x0
Known
eb789..
andER
:
∀ x0 x1 : ο .
and
x0
x1
⟶
x1
Known
c1173..
Subq_def
:
Subq
=
λ x1 x2 .
∀ x3 .
In
x3
x1
⟶
In
x3
x2
Known
7f305..
EmptyAx
:
not
(
∀ x0 : ο .
(
∀ x1 .
In
x1
0
⟶
x0
)
⟶
x0
)
Known
b4782..
contra
:
∀ x0 : ο .
(
not
x0
⟶
False
)
⟶
x0
Known
e7295..
:
∀ x0 x1 : ο .
x0
=
x1
⟶
and
(
x0
⟶
x1
)
(
x1
⟶
x0
)
Known
notE
notE
:
∀ x0 : ο .
not
x0
⟶
x0
⟶
False
Known
8106d..
notI
:
∀ x0 : ο .
(
x0
⟶
False
)
⟶
not
x0
Known
fcbcf..
not_all_ex_demorgan_i
:
∀ x0 :
ι → ο
.
not
(
∀ x1 .
x0
x1
)
⟶
∀ x1 : ο .
(
∀ x2 .
not
(
x0
x2
)
⟶
x1
)
⟶
x1
Known
5f823..
not_ex_all_demorgan_i
:
∀ x0 :
ι → ο
.
not
(
∀ x1 : ο .
(
∀ x2 .
x0
x2
⟶
x1
)
⟶
x1
)
⟶
∀ x1 .
not
(
x0
x1
)
Known
0ff1b..
:
∀ x0 x1 : ο .
not
(
x0
⟶
x1
)
⟶
and
x0
(
not
x1
)
Known
91bfe..
dnegI
:
∀ x0 : ο .
x0
⟶
not
(
not
x0
)
Known
5232a..
:
∀ x0 x1 : ο .
(
x0
⟶
x1
)
⟶
not
x1
⟶
not
x0
Theorem
453a2..
:
(
∀ x0 .
Subq
x0
(
setsum
(
Inj0
(
SNoLev
(
binrep
(
Power
(
Power
(
Power
0
)
)
)
0
)
)
)
(
Power
(
Power
(
Power
(
Power
0
)
)
)
)
)
⟶
∀ x1 : ο .
(
∀ x2 .
and
(
In
x2
x0
)
(
∀ x3 .
(
(
∀ x4 .
(
∀ x5 : ο .
(
∀ x6 .
and
(
Subq
x6
x0
)
(
(
(
exactly5
x4
⟶
not
(
exactly2
x3
)
)
⟶
(
exactly3
x4
⟶
not
(
SNo
x4
)
)
⟶
not
(
atleast6
x4
)
)
⟶
not
(
exactly4
x6
)
)
⟶
x5
)
⟶
x5
)
⟶
not
(
exactly4
x2
)
)
⟶
atleast2
(
binrep
(
binrep
(
Power
(
binrep
(
Power
(
Power
0
)
)
0
)
)
(
Power
(
Power
0
)
)
)
0
)
)
⟶
not
(
Subq
x3
x2
)
)
⟶
x1
)
⟶
x1
)
⟶
∀ x0 : ο .
x0
(proof)