Search for blocks/addresses/...
Proofgold Signed Transaction
vin
Pr7tr..
/
92601..
PUeHC..
/
4c6f4..
vout
Pr7tr..
/
26c58..
6.06 bars
TMQAb..
/
aaa55..
ownership of
48ba7..
as prop with payaddr
Pr4zB..
rights free controlledby
Pr4zB..
upto 0
TMStU..
/
48421..
ownership of
8f7d8..
as prop with payaddr
Pr4zB..
rights free controlledby
Pr4zB..
upto 0
TMH3g..
/
72448..
ownership of
b0f83..
as prop with payaddr
Pr4zB..
rights free controlledby
Pr4zB..
upto 0
TMd8Y..
/
fb885..
ownership of
9d497..
as prop with payaddr
Pr4zB..
rights free controlledby
Pr4zB..
upto 0
TMbGa..
/
0f09a..
ownership of
0e32a..
as prop with payaddr
Pr4zB..
rights free controlledby
Pr4zB..
upto 0
TMKeM..
/
d5d4b..
ownership of
b2c76..
as prop with payaddr
Pr4zB..
rights free controlledby
Pr4zB..
upto 0
TMbrz..
/
3d2fb..
ownership of
ce03f..
as prop with payaddr
Pr4zB..
rights free controlledby
Pr4zB..
upto 0
TMWpx..
/
59b43..
ownership of
27bc1..
as prop with payaddr
Pr4zB..
rights free controlledby
Pr4zB..
upto 0
TMJK7..
/
1233f..
ownership of
1dd52..
as prop with payaddr
Pr4zB..
rights free controlledby
Pr4zB..
upto 0
TMRDp..
/
2b9b1..
ownership of
ab4d6..
as prop with payaddr
Pr4zB..
rights free controlledby
Pr4zB..
upto 0
TMEq2..
/
3293a..
ownership of
9f26e..
as prop with payaddr
Pr4zB..
rights free controlledby
Pr4zB..
upto 0
TMTDc..
/
deae3..
ownership of
db81c..
as prop with payaddr
Pr4zB..
rights free controlledby
Pr4zB..
upto 0
PUeFj..
/
6c0ee..
doc published by
Pr4zB..
Param
ap
ap
:
ι
→
ι
→
ι
Param
lam
Sigma
:
ι
→
(
ι
→
ι
) →
ι
Param
ordsucc
ordsucc
:
ι
→
ι
Param
If_i
If_i
:
ο
→
ι
→
ι
→
ι
Definition
u17_to_Church17
:=
λ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 .
ap
(
lam
17
(
λ x18 .
If_i
(
x18
=
0
)
x1
(
If_i
(
x18
=
1
)
x2
(
If_i
(
x18
=
2
)
x3
(
If_i
(
x18
=
3
)
x4
(
If_i
(
x18
=
4
)
x5
(
If_i
(
x18
=
5
)
x6
(
If_i
(
x18
=
6
)
x7
(
If_i
(
x18
=
7
)
x8
(
If_i
(
x18
=
8
)
x9
(
If_i
(
x18
=
9
)
x10
(
If_i
(
x18
=
10
)
x11
(
If_i
(
x18
=
11
)
x12
(
If_i
(
x18
=
12
)
x13
(
If_i
(
x18
=
13
)
x14
(
If_i
(
x18
=
14
)
x15
(
If_i
(
x18
=
15
)
x16
x17
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
x0
Param
u6
:
ι
Known
5af4c..
:
(
∀ x0 x1 .
∀ x2 :
ι →
ι → ι
.
∀ x3 .
x3
∈
x1
⟶
ap
(
lam
x1
(
λ x5 .
If_i
(
x5
=
x3
)
x0
(
x2
(
ordsucc
x3
)
x5
)
)
)
x3
=
x0
)
⟶
(
∀ x0 x1 .
∀ x2 :
ι →
ι → ι
.
∀ x3 x4 .
(
x4
=
x3
⟶
∀ x5 : ο .
x5
)
⟶
ap
(
lam
x1
(
λ x6 .
If_i
(
x6
=
x3
)
x0
(
x2
(
ordsucc
x3
)
x6
)
)
)
x4
=
ap
(
lam
x1
(
x2
(
ordsucc
x3
)
)
)
x4
)
⟶
∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 .
ap
(
lam
17
(
λ x18 .
If_i
(
x18
=
0
)
x0
(
If_i
(
x18
=
1
)
x1
(
If_i
(
x18
=
2
)
x2
(
If_i
(
x18
=
3
)
x3
(
If_i
(
x18
=
4
)
x4
(
If_i
(
x18
=
5
)
x5
(
If_i
(
x18
=
6
)
x6
(
If_i
(
x18
=
7
)
x7
(
If_i
(
x18
=
8
)
x8
(
If_i
(
x18
=
9
)
x9
(
If_i
(
x18
=
10
)
x10
(
If_i
(
x18
=
11
)
x11
(
If_i
(
x18
=
12
)
x12
(
If_i
(
x18
=
13
)
x13
(
If_i
(
x18
=
14
)
x14
(
If_i
(
x18
=
15
)
x15
x16
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
u6
=
x6
Known
48efb..
:
∀ x0 x1 .
∀ x2 :
ι →
ι → ι
.
∀ x3 .
x3
∈
x1
⟶
ap
(
lam
x1
(
λ x5 .
If_i
(
x5
=
x3
)
x0
(
x2
(
ordsucc
x3
)
x5
)
)
)
x3
=
x0
Known
d21a1..
:
∀ x0 x1 .
∀ x2 :
ι →
ι → ι
.
∀ x3 x4 .
(
x4
=
x3
⟶
∀ x5 : ο .
x5
)
⟶
ap
(
lam
x1
(
λ x6 .
If_i
(
x6
=
x3
)
x0
(
x2
(
ordsucc
x3
)
x6
)
)
)
x4
=
ap
(
lam
x1
(
x2
(
ordsucc
x3
)
)
)
x4
Theorem
9f26e..
:
∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 .
ap
(
lam
17
(
λ x18 .
If_i
(
x18
=
0
)
x0
(
If_i
(
x18
=
1
)
x1
(
If_i
(
x18
=
2
)
x2
(
If_i
(
x18
=
3
)
x3
(
If_i
(
x18
=
4
)
x4
(
If_i
(
x18
=
5
)
x5
(
If_i
(
x18
=
6
)
x6
(
If_i
(
x18
=
7
)
x7
(
If_i
(
x18
=
8
)
x8
(
If_i
(
x18
=
9
)
x9
(
If_i
(
x18
=
10
)
x10
(
If_i
(
x18
=
11
)
x11
(
If_i
(
x18
=
12
)
x12
(
If_i
(
x18
=
13
)
x13
(
If_i
(
x18
=
14
)
x14
(
If_i
(
x18
=
15
)
x15
x16
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
u6
=
x6
...
Param
u7
:
ι
Known
63896..
:
(
∀ x0 x1 .
∀ x2 :
ι →
ι → ι
.
∀ x3 .
x3
∈
x1
⟶
ap
(
lam
x1
(
λ x5 .
If_i
(
x5
=
x3
)
x0
(
x2
(
ordsucc
x3
)
x5
)
)
)
x3
=
x0
)
⟶
(
∀ x0 x1 .
∀ x2 :
ι →
ι → ι
.
∀ x3 x4 .
(
x4
=
x3
⟶
∀ x5 : ο .
x5
)
⟶
ap
(
lam
x1
(
λ x6 .
If_i
(
x6
=
x3
)
x0
(
x2
(
ordsucc
x3
)
x6
)
)
)
x4
=
ap
(
lam
x1
(
x2
(
ordsucc
x3
)
)
)
x4
)
⟶
∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 .
ap
(
lam
17
(
λ x18 .
If_i
(
x18
=
0
)
x0
(
If_i
(
x18
=
1
)
x1
(
If_i
(
x18
=
2
)
x2
(
If_i
(
x18
=
3
)
x3
(
If_i
(
x18
=
4
)
x4
(
If_i
(
x18
=
5
)
x5
(
If_i
(
x18
=
6
)
x6
(
If_i
(
x18
=
7
)
x7
(
If_i
(
x18
=
8
)
x8
(
If_i
(
x18
=
9
)
x9
(
If_i
(
x18
=
10
)
x10
(
If_i
(
x18
=
11
)
x11
(
If_i
(
x18
=
12
)
x12
(
If_i
(
x18
=
13
)
x13
(
If_i
(
x18
=
14
)
x14
(
If_i
(
x18
=
15
)
x15
x16
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
u7
=
x7
Theorem
1dd52..
:
∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 .
ap
(
lam
17
(
λ x18 .
If_i
(
x18
=
0
)
x0
(
If_i
(
x18
=
1
)
x1
(
If_i
(
x18
=
2
)
x2
(
If_i
(
x18
=
3
)
x3
(
If_i
(
x18
=
4
)
x4
(
If_i
(
x18
=
5
)
x5
(
If_i
(
x18
=
6
)
x6
(
If_i
(
x18
=
7
)
x7
(
If_i
(
x18
=
8
)
x8
(
If_i
(
x18
=
9
)
x9
(
If_i
(
x18
=
10
)
x10
(
If_i
(
x18
=
11
)
x11
(
If_i
(
x18
=
12
)
x12
(
If_i
(
x18
=
13
)
x13
(
If_i
(
x18
=
14
)
x14
(
If_i
(
x18
=
15
)
x15
x16
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
u7
=
x7
...
Param
u8
:
ι
Known
9c74a..
:
(
∀ x0 x1 .
∀ x2 :
ι →
ι → ι
.
∀ x3 .
x3
∈
x1
⟶
ap
(
lam
x1
(
λ x5 .
If_i
(
x5
=
x3
)
x0
(
x2
(
ordsucc
x3
)
x5
)
)
)
x3
=
x0
)
⟶
(
∀ x0 x1 .
∀ x2 :
ι →
ι → ι
.
∀ x3 x4 .
(
x4
=
x3
⟶
∀ x5 : ο .
x5
)
⟶
ap
(
lam
x1
(
λ x6 .
If_i
(
x6
=
x3
)
x0
(
x2
(
ordsucc
x3
)
x6
)
)
)
x4
=
ap
(
lam
x1
(
x2
(
ordsucc
x3
)
)
)
x4
)
⟶
∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 .
ap
(
lam
17
(
λ x18 .
If_i
(
x18
=
0
)
x0
(
If_i
(
x18
=
1
)
x1
(
If_i
(
x18
=
2
)
x2
(
If_i
(
x18
=
3
)
x3
(
If_i
(
x18
=
4
)
x4
(
If_i
(
x18
=
5
)
x5
(
If_i
(
x18
=
6
)
x6
(
If_i
(
x18
=
7
)
x7
(
If_i
(
x18
=
8
)
x8
(
If_i
(
x18
=
9
)
x9
(
If_i
(
x18
=
10
)
x10
(
If_i
(
x18
=
11
)
x11
(
If_i
(
x18
=
12
)
x12
(
If_i
(
x18
=
13
)
x13
(
If_i
(
x18
=
14
)
x14
(
If_i
(
x18
=
15
)
x15
x16
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
u8
=
x8
Theorem
ce03f..
:
∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 .
ap
(
lam
17
(
λ x18 .
If_i
(
x18
=
0
)
x0
(
If_i
(
x18
=
1
)
x1
(
If_i
(
x18
=
2
)
x2
(
If_i
(
x18
=
3
)
x3
(
If_i
(
x18
=
4
)
x4
(
If_i
(
x18
=
5
)
x5
(
If_i
(
x18
=
6
)
x6
(
If_i
(
x18
=
7
)
x7
(
If_i
(
x18
=
8
)
x8
(
If_i
(
x18
=
9
)
x9
(
If_i
(
x18
=
10
)
x10
(
If_i
(
x18
=
11
)
x11
(
If_i
(
x18
=
12
)
x12
(
If_i
(
x18
=
13
)
x13
(
If_i
(
x18
=
14
)
x14
(
If_i
(
x18
=
15
)
x15
x16
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
u8
=
x8
...
Known
aa7c9..
:
∀ x0 :
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι → ι
.
∀ x1 .
∀ x2 :
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι → ι
.
(
∀ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 .
x0
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
x14
x15
x16
x17
x18
x19
=
x2
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
x14
x15
x16
x17
x18
x19
)
⟶
x0
x1
=
x2
Theorem
0e32a..
:
u17_to_Church17
u6
=
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 .
x7
...
Theorem
b0f83..
:
u17_to_Church17
u7
=
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 .
x8
...
Theorem
48ba7..
:
u17_to_Church17
u8
=
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 .
x9
...