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Proofgold Asset
asset id
9a53a9d6d902ca66a00e4735c52bfc9d06b203ce06cd2ac6177c3cdff3cbb322
asset hash
376cf43aea7fb6c1b34676578ef93628ad1117823881b055e4d496b8c9747dbf
bday / block
3180
tx
49665..
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
5f006..
:
∀ x0 .
Subq
x0
(
binrep
(
Power
(
binrep
(
Power
(
Power
0
)
)
0
)
)
(
Power
(
Power
0
)
)
)
⟶
∀ x1 : ο .
(
∀ x2 .
(
(
∀ x3 : ο .
(
∀ x4 .
and
(
∀ x5 .
SNo_
x0
(
binrep
(
Power
(
Power
(
Power
(
Power
0
)
)
)
)
0
)
⟶
∀ x6 .
not
(
atleast4
x5
)
)
(
∀ x5 .
Subq
x5
x2
⟶
∀ x6 : ο .
(
∀ x7 .
and
(
In
x7
(
Inj0
(
binrep
(
Power
(
Power
(
Power
0
)
)
)
0
)
)
)
(
and
(
(
atleast6
x5
⟶
not
(
set_of_pairs
x7
)
)
⟶
and
(
atleast6
x7
)
(
not
(
exactly4
x5
)
)
)
(
and
(
not
(
exactly2
x7
)
)
(
not
(
Subq
0
x4
)
)
)
)
⟶
x6
)
⟶
x6
)
⟶
x3
)
⟶
x3
)
⟶
∀ x3 : ο .
(
∀ x4 .
and
(
Subq
x4
(
binrep
(
binrep
(
Power
(
Power
(
Power
0
)
)
)
(
Power
0
)
)
0
)
)
(
ordinal
0
)
⟶
x3
)
⟶
x3
)
⟶
x1
)
⟶
x1
(proof)