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Proofgold Asset
asset id
5cbbb7001eed9060d637f1dbfb0881373001cf9e17ecb7aeaf4b4f76b2df0d5b
asset hash
481081fd4b9cf8b5aec79a6c77d618c79e17f8b2322c269b735b3896f471db83
bday / block
2058
tx
f0c21..
preasset
doc published by
PrGxv..
Param
and
:
ο
→
ο
→
ο
Param
5d0c6..
:
(
ι
→
ι
→
ο
) →
ο
Param
True
:
ο
Definition
db882..
:=
λ x0 :
ι →
ι → ο
.
and
(
5d0c6..
x0
)
True
Param
29aed..
:
(
ι
→
ι
→
ο
) →
ο
Definition
46c0e..
:=
λ x0 :
ι →
ι → ο
.
and
(
29aed..
x0
)
True
Definition
81a9b..
:=
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x1
x1
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x0
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x0
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x1
x1
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x0
)
)
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x0
x1
)
(
prim0
x1
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x0
)
)
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x0
)
)
(
prim0
(
prim0
x1
x1
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x0
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x0
)
)
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x0
)
)
(
prim0
(
prim0
x1
x1
)
(
prim0
x0
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x0
)
)
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x0
)
)
)
)
)
(
prim1
(
λ x0 .
x0
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
Param
57d6a..
:
ι
→
ι
→
ι
Param
67ee8..
:
ι
Param
25ca3..
:
ι
Param
5b8fe..
:
ι
Definition
b72ce..
:=
57d6a..
67ee8..
(
57d6a..
25ca3..
5b8fe..
)
Param
7a0ec..
:
ι
Param
bcddf..
:
ι
→
(
ι
→
ι
) →
ι
Param
f3baa..
:
ι
Definition
9f288..
:=
57d6a..
(
57d6a..
7a0ec..
5b8fe..
)
(
bcddf..
(
57d6a..
67ee8..
(
57d6a..
25ca3..
5b8fe..
)
)
(
λ x0 .
57d6a..
(
57d6a..
f3baa..
x0
)
x0
)
)
Definition
eb3d5..
:=
λ x0 :
ι →
ι → ο
.
and
(
db882..
x0
)
(
x0
81a9b..
b72ce..
)
Param
d478c..
:
(
ι
→
ι
→
ο
) →
(
ι
→
ι
→
ο
) →
ι
→
ο
Conjecture
97d81..
:
∀ x0 x1 :
ι →
ι → ο
.
db882..
x0
⟶
46c0e..
x1
⟶
d478c..
x0
x1
b72ce..
Param
6fe8d..
:
(
ι
→
ι
→
ο
) →
(
ι
→
ι
→
ο
) →
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ο
Param
5c39b..
:
ι
→
ι
→
ο
Conjecture
24deb..
:
∀ x0 x1 :
ι →
ι → ο
.
db882..
x0
⟶
46c0e..
x1
⟶
6fe8d..
x0
x1
5c39b..
9f288..
b72ce..
Definition
0af41..
:=
λ x0 :
ι →
ι → ο
.
and
(
46c0e..
x0
)
(
x0
81a9b..
9f288..
)
Definition
ae581..
:=
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x1
x1
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x0
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x0
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x1
x1
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x0
)
)
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x0
x1
)
(
prim0
x1
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x0
)
)
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x0
)
)
(
prim0
(
prim0
x1
x1
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x0
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x1
)
)
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x1
x1
)
(
prim0
x1
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x1
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x0
)
)
(
prim0
(
prim0
x1
x1
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x0
)
)
)
)
)
(
prim1
(
λ x0 .
x0
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
Definition
b72ce..
:=
57d6a..
67ee8..
(
57d6a..
25ca3..
5b8fe..
)
Definition
43ba7..
:=
57d6a..
(
57d6a..
7a0ec..
5b8fe..
)
(
bcddf..
(
57d6a..
67ee8..
(
57d6a..
25ca3..
5b8fe..
)
)
(
λ x0 .
x0
)
)
Definition
f0a4f..
:=
λ x0 :
ι →
ι → ο
.
and
(
eb3d5..
x0
)
(
x0
ae581..
b72ce..
)
Conjecture
f59f8..
:
∀ x0 x1 :
ι →
ι → ο
.
eb3d5..
x0
⟶
0af41..
x1
⟶
d478c..
x0
x1
b72ce..
Conjecture
7bc07..
:
∀ x0 x1 :
ι →
ι → ο
.
eb3d5..
x0
⟶
0af41..
x1
⟶
6fe8d..
x0
x1
5c39b..
43ba7..
b72ce..
Definition
6c8dd..
:=
λ x0 :
ι →
ι → ο
.
and
(
0af41..
x0
)
(
x0
ae581..
43ba7..
)
Definition
a9a29..
:=
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x1
x1
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x0
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x0
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x1
x1
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x0
)
)
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x0
x1
)
(
prim0
x1
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x0
)
)
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x0
)
)
(
prim0
(
prim0
x1
x1
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x0
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x1
)
)
(
prim0
(
prim0
x0
x1
)
(
prim0
x1
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x1
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x0
)
)
(
prim0
(
prim0
x1
x1
)
(
prim0
x1
x1
)
)
)
)
)
(
prim1
(
λ x0 .
x0
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
Param
62f06..
:
ι
Definition
8f3a7..
:=
57d6a..
67ee8..
(
57d6a..
25ca3..
(
57d6a..
(
57d6a..
62f06..
5b8fe..
)
(
57d6a..
(
57d6a..
62f06..
5b8fe..
)
5b8fe..
)
)
)
Definition
3569a..
:=
bcddf..
(
57d6a..
67ee8..
(
57d6a..
25ca3..
5b8fe..
)
)
(
λ x0 .
bcddf..
(
57d6a..
67ee8..
(
57d6a..
25ca3..
5b8fe..
)
)
(
57d6a..
(
57d6a..
f3baa..
x0
)
)
)
Definition
1efc7..
:=
λ x0 :
ι →
ι → ο
.
and
(
f0a4f..
x0
)
(
x0
a9a29..
8f3a7..
)
Conjecture
042d9..
:
∀ x0 x1 :
ι →
ι → ο
.
f0a4f..
x0
⟶
6c8dd..
x1
⟶
d478c..
x0
x1
8f3a7..
Conjecture
233d8..
:
∀ x0 x1 :
ι →
ι → ο
.
f0a4f..
x0
⟶
6c8dd..
x1
⟶
6fe8d..
x0
x1
5c39b..
3569a..
8f3a7..
Definition
be8f5..
:=
λ x0 :
ι →
ι → ο
.
and
(
6c8dd..
x0
)
(
x0
a9a29..
3569a..
)
Definition
c8911..
:=
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x1
x1
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x0
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x0
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x1
x1
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x0
)
)
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x0
x1
)
(
prim0
x1
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x0
)
)
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x0
)
)
(
prim0
(
prim0
x1
x1
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x0
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x1
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x0
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x0
)
)
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x1
)
)
)
)
)
(
prim1
(
λ x0 .
x0
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
Definition
fb4c3..
:=
57d6a..
67ee8..
(
57d6a..
25ca3..
(
57d6a..
(
57d6a..
62f06..
5b8fe..
)
5b8fe..
)
)
Definition
ff75b..
:=
bcddf..
(
57d6a..
67ee8..
(
57d6a..
25ca3..
5b8fe..
)
)
(
λ x0 .
57d6a..
(
57d6a..
f3baa..
x0
)
ae581..
)
Definition
31c5d..
:=
λ x0 :
ι →
ι → ο
.
and
(
1efc7..
x0
)
(
x0
c8911..
fb4c3..
)
Conjecture
ec382..
:
∀ x0 x1 :
ι →
ι → ο
.
1efc7..
x0
⟶
be8f5..
x1
⟶
d478c..
x0
x1
fb4c3..
Conjecture
3fed5..
:
∀ x0 x1 :
ι →
ι → ο
.
1efc7..
x0
⟶
be8f5..
x1
⟶
6fe8d..
x0
x1
5c39b..
ff75b..
fb4c3..
Definition
0ae4d..
:=
λ x0 :
ι →
ι → ο
.
and
(
be8f5..
x0
)
(
x0
c8911..
ff75b..
)
Definition
2f6f1..
:=
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x1
x1
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x0
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x0
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x1
x1
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x0
)
)
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x0
x1
)
(
prim0
x1
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x0
)
)
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x0
)
)
(
prim0
(
prim0
x1
x1
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x0
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x1
)
)
(
prim0
(
prim0
x1
x1
)
(
prim0
x1
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x0
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x1
)
)
)
)
)
(
prim1
(
λ x0 .
x0
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
Definition
8f3a7..
:=
57d6a..
67ee8..
(
57d6a..
25ca3..
(
57d6a..
(
57d6a..
62f06..
5b8fe..
)
(
57d6a..
(
57d6a..
62f06..
5b8fe..
)
5b8fe..
)
)
)
Definition
80bb2..
:=
bcddf..
(
57d6a..
67ee8..
(
57d6a..
25ca3..
5b8fe..
)
)
(
λ x0 .
bcddf..
(
57d6a..
67ee8..
(
57d6a..
25ca3..
5b8fe..
)
)
(
λ x1 .
57d6a..
(
57d6a..
7a0ec..
5b8fe..
)
(
bcddf..
(
57d6a..
67ee8..
(
57d6a..
25ca3..
5b8fe..
)
)
(
λ x2 .
57d6a..
(
57d6a..
f3baa..
(
57d6a..
(
57d6a..
f3baa..
x0
)
(
57d6a..
(
57d6a..
f3baa..
x1
)
x2
)
)
)
x2
)
)
)
)
Definition
ed300..
:=
λ x0 :
ι →
ι → ο
.
and
(
31c5d..
x0
)
(
x0
2f6f1..
8f3a7..
)
Conjecture
caf82..
:
∀ x0 x1 :
ι →
ι → ο
.
31c5d..
x0
⟶
0ae4d..
x1
⟶
d478c..
x0
x1
8f3a7..
Conjecture
e4488..
:
∀ x0 x1 :
ι →
ι → ο
.
31c5d..
x0
⟶
0ae4d..
x1
⟶
6fe8d..
x0
x1
5c39b..
80bb2..
8f3a7..
Definition
b3fef..
:=
λ x0 :
ι →
ι → ο
.
and
(
0ae4d..
x0
)
(
x0
2f6f1..
80bb2..
)
Definition
62b32..
:=
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x1
x1
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x0
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x0
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x1
x1
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x0
)
)
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x0
x1
)
(
prim0
x1
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x0
)
)
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x0
)
)
(
prim0
(
prim0
x1
x1
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x0
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x1
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x0
)
)
(
prim0
(
prim0
x1
x1
)
(
prim0
x0
x1
)
)
)
)
)
(
prim1
(
λ x0 .
x0
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
Definition
8f3a7..
:=
57d6a..
67ee8..
(
57d6a..
25ca3..
(
57d6a..
(
57d6a..
62f06..
5b8fe..
)
(
57d6a..
(
57d6a..
62f06..
5b8fe..
)
5b8fe..
)
)
)
Definition
49b5c..
:=
bcddf..
(
57d6a..
67ee8..
(
57d6a..
25ca3..
5b8fe..
)
)
(
λ x0 .
bcddf..
(
57d6a..
67ee8..
(
57d6a..
25ca3..
5b8fe..
)
)
(
λ x1 .
57d6a..
(
57d6a..
7a0ec..
5b8fe..
)
(
bcddf..
(
57d6a..
67ee8..
(
57d6a..
25ca3..
5b8fe..
)
)
(
λ x2 .
57d6a..
(
57d6a..
f3baa..
(
57d6a..
(
57d6a..
f3baa..
x0
)
x2
)
)
(
57d6a..
(
57d6a..
f3baa..
(
57d6a..
(
57d6a..
f3baa..
x1
)
x2
)
)
x2
)
)
)
)
)
Definition
31a35..
:=
λ x0 :
ι →
ι → ο
.
and
(
ed300..
x0
)
(
x0
62b32..
8f3a7..
)
Conjecture
3f3b3..
:
∀ x0 x1 :
ι →
ι → ο
.
ed300..
x0
⟶
b3fef..
x1
⟶
d478c..
x0
x1
8f3a7..
Conjecture
f34bd..
:
∀ x0 x1 :
ι →
ι → ο
.
ed300..
x0
⟶
b3fef..
x1
⟶
6fe8d..
x0
x1
5c39b..
49b5c..
8f3a7..
Definition
ffd30..
:=
λ x0 :
ι →
ι → ο
.
and
(
b3fef..
x0
)
(
x0
62b32..
49b5c..
)
Definition
36978..
:=
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x1
x1
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x0
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x0
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x1
x1
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x0
)
)
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x0
x1
)
(
prim0
x1
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x0
)
)
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x0
)
)
(
prim0
(
prim0
x1
x1
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x0
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x1
)
)
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x0
)
)
(
prim0
(
prim0
x0
x1
)
(
prim0
x1
x1
)
)
)
)
)
(
prim1
(
λ x0 .
x0
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
Param
27862..
:
ι
Param
1f2c4..
:
ι
Definition
6e624..
:=
57d6a..
67ee8..
(
57d6a..
27862..
(
bcddf..
1f2c4..
(
λ x0 .
57d6a..
25ca3..
(
57d6a..
(
57d6a..
62f06..
(
57d6a..
(
57d6a..
62f06..
x0
)
5b8fe..
)
)
5b8fe..
)
)
)
)
Definition
b9ba9..
:=
bcddf..
1f2c4..
(
λ x0 .
bcddf..
(
57d6a..
67ee8..
(
57d6a..
25ca3..
(
57d6a..
(
57d6a..
62f06..
x0
)
5b8fe..
)
)
)
(
λ x1 .
57d6a..
(
57d6a..
7a0ec..
5b8fe..
)
(
bcddf..
(
57d6a..
67ee8..
(
57d6a..
25ca3..
5b8fe..
)
)
(
57d6a..
(
57d6a..
f3baa..
(
57d6a..
(
57d6a..
7a0ec..
x0
)
(
bcddf..
(
57d6a..
67ee8..
(
57d6a..
25ca3..
x0
)
)
(
λ x2 .
57d6a..
(
57d6a..
f3baa..
(
57d6a..
x1
x2
)
)
x2
)
)
)
)
)
)
)
)
Definition
b2995..
:=
λ x0 :
ι →
ι → ο
.
and
(
31a35..
x0
)
(
x0
36978..
6e624..
)
Conjecture
599ee..
:
∀ x0 x1 :
ι →
ι → ο
.
31a35..
x0
⟶
ffd30..
x1
⟶
d478c..
x0
x1
6e624..
Conjecture
e531a..
:
∀ x0 x1 :
ι →
ι → ο
.
31a35..
x0
⟶
ffd30..
x1
⟶
6fe8d..
x0
x1
5c39b..
b9ba9..
6e624..
Definition
a604f..
:=
λ x0 :
ι →
ι → ο
.
and
(
ffd30..
x0
)
(
x0
36978..
b9ba9..
)
Definition
00c71..
:=
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x1
x1
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x0
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x0
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x1
x1
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x0
)
)
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x0
x1
)
(
prim0
x1
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x0
)
)
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x0
)
)
(
prim0
(
prim0
x1
x1
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x0
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x1
)
)
(
prim0
(
prim0
x0
x1
)
(
prim0
x1
x0
)
)
)
)
)
(
prim1
(
λ x0 .
x0
)
)
)
)
)
)
)
)
)
)
)
)
)
)
Param
3cd3c..
:
ι
Definition
00b46..
:=
57d6a..
3cd3c..
81a9b..
Definition
11543..
:=
bcddf..
(
57d6a..
67ee8..
(
57d6a..
25ca3..
5b8fe..
)
)
(
λ x0 .
bcddf..
(
57d6a..
3cd3c..
x0
)
(
λ x1 .
x1
)
)
Definition
244aa..
:=
λ x0 :
ι →
ι → ο
.
and
(
b2995..
x0
)
(
x0
00c71..
00b46..
)
Conjecture
65921..
:
∀ x0 x1 :
ι →
ι → ο
.
b2995..
x0
⟶
a604f..
x1
⟶
d478c..
x0
x1
00b46..
Conjecture
9421d..
:
∀ x0 x1 :
ι →
ι → ο
.
b2995..
x0
⟶
a604f..
x1
⟶
6fe8d..
x0
x1
5c39b..
11543..
00b46..
Definition
39ffe..
:=
λ x0 :
ι →
ι → ο
.
and
(
a604f..
x0
)
(
x0
00c71..
11543..
)
Definition
244aa..
:=
244aa..
Definition
39ffe..
:=
39ffe..