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Proofgold Asset
asset id
fe90b40e8f091dd585c7830d0747e46448d4388c7bcaf50a2adedf6151d9b5fa
asset hash
f64f162104158816b9ecf9d8e0157ef142f4a4489d96cb36b767b6e5eb89feb2
bday / block
1995
tx
ca03b..
preasset
doc published by
PrGxv..
Param
True
:
ο
Definition
bb8e6..
:=
λ x0 :
ι →
ι → ο
.
True
Definition
bb8e6..
:=
λ x0 :
ι →
ι → ο
.
True
Definition
1f2c4..
:=
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
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
x0
)
(
prim0
x1
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
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
x1
x0
)
)
(
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
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x0
)
)
(
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
x1
)
(
prim0
x1
x1
)
)
)
)
)
(
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
32d20..
:
ι
Definition
32d20..
:=
32d20..
Param
and
:
ο
→
ο
→
ο
Definition
934b2..
:=
λ x0 :
ι →
ι → ο
.
and
(
bb8e6..
x0
)
(
x0
1f2c4..
32d20..
)
Param
d478c..
:
(
ι
→
ι
→
ο
) →
(
ι
→
ι
→
ο
) →
ι
→
ο
Conjecture
a1ac9..
:
∀ x0 x1 :
ι →
ι → ο
.
bb8e6..
x0
⟶
bb8e6..
x1
⟶
d478c..
x0
x1
32d20..
Definition
62f06..
:=
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
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
x0
)
(
prim0
x1
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
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
x1
x0
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x0
x0
)
)
)
)
)
(
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
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
x1
)
(
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
x0
x0
)
)
)
)
)
(
prim1
(
λ x0 .
x0
)
)
)
)
)
)
)
)
)
)
)
)
Param
91fd5..
:
ι
→
ι
→
ι
Definition
48ac8..
:=
91fd5..
1f2c4..
(
91fd5..
1f2c4..
1f2c4..
)
Definition
edc3c..
:=
λ x0 :
ι →
ι → ο
.
and
(
934b2..
x0
)
(
x0
62f06..
48ac8..
)
Conjecture
75198..
:
∀ x0 x1 :
ι →
ι → ο
.
934b2..
x0
⟶
bb8e6..
x1
⟶
d478c..
x0
x1
48ac8..
Definition
5b8fe..
:=
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
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
x0
)
(
prim0
x1
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
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
x1
x0
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x1
x1
)
(
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
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
x1
x1
)
)
)
)
)
(
prim1
(
λ x0 .
x0
)
)
)
)
)
)
)
)
)
)
)
Definition
1f2c4..
:=
1f2c4..
Definition
ffdc7..
:=
λ x0 :
ι →
ι → ο
.
and
(
edc3c..
x0
)
(
x0
5b8fe..
1f2c4..
)
Conjecture
f6498..
:
∀ x0 x1 :
ι →
ι → ο
.
edc3c..
x0
⟶
bb8e6..
x1
⟶
d478c..
x0
x1
1f2c4..
Definition
67794..
:=
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
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
x0
)
(
prim0
x1
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
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
x1
x0
)
)
(
prim0
(
prim0
x0
x0
)
(
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
)
)
)
)
)
(
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
x1
x1
)
(
prim0
x1
x0
)
)
)
)
)
(
prim1
(
λ x0 .
x0
)
)
)
)
)
)
)
)
)
)
Definition
302e5..
:=
91fd5..
1f2c4..
32d20..
Definition
61af4..
:=
λ x0 :
ι →
ι → ο
.
and
(
ffdc7..
x0
)
(
x0
67794..
302e5..
)
Conjecture
51037..
:
∀ x0 x1 :
ι →
ι → ο
.
ffdc7..
x0
⟶
bb8e6..
x1
⟶
d478c..
x0
x1
302e5..
Definition
e36e8..
:=
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
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
x0
)
(
prim0
x1
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
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
x1
x0
)
)
(
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
x1
x1
)
)
)
)
)
(
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
x0
)
)
(
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
x1
)
(
prim0
x1
x1
)
)
)
)
)
(
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
32d20..
:=
32d20..
Definition
4a50e..
:=
λ x0 :
ι →
ι → ο
.
and
(
61af4..
x0
)
(
x0
e36e8..
32d20..
)
Conjecture
3b7e7..
:
∀ x0 x1 :
ι →
ι → ο
.
61af4..
x0
⟶
bb8e6..
x1
⟶
d478c..
x0
x1
32d20..
Definition
25ca3..
:=
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
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
x0
)
(
prim0
x1
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
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
x1
x0
)
)
(
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
x1
x1
)
)
)
)
)
(
prim1
(
λ x0 .
x0
)
)
)
)
)
)
)
)
Definition
f2088..
:=
91fd5..
1f2c4..
e36e8..
Definition
0c961..
:=
λ x0 :
ι →
ι → ο
.
and
(
4a50e..
x0
)
(
x0
25ca3..
f2088..
)
Conjecture
3fadb..
:
∀ x0 x1 :
ι →
ι → ο
.
4a50e..
x0
⟶
bb8e6..
x1
⟶
d478c..
x0
x1
f2088..
Definition
67ee8..
:=
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
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
x0
)
(
prim0
x1
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
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
x1
x0
)
)
(
prim0
(
prim0
x0
x0
)
(
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
)
)
)
)
)
(
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
x1
x1
)
(
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
)
)
)
)
)
)
)
)
)
)
)
Definition
d7c0d..
:=
91fd5..
e36e8..
32d20..
Definition
d6106..
:=
λ x0 :
ι →
ι → ο
.
and
(
0c961..
x0
)
(
x0
67ee8..
d7c0d..
)
Conjecture
ddcd3..
:
∀ x0 x1 :
ι →
ι → ο
.
0c961..
x0
⟶
bb8e6..
x1
⟶
d478c..
x0
x1
d7c0d..
Definition
27862..
:=
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
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
x0
)
(
prim0
x1
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
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
x1
x0
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
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
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
)
)
)
)
)
(
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
x1
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x1
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x1
)
)
(
prim0
(
prim0
x0
x1
)
(
prim0
x0
x0
)
)
)
)
)
(
prim1
(
λ x0 .
x0
)
)
)
)
)
)
)
)
)
)
)
)
)
)
Definition
1b59f..
:=
91fd5..
(
91fd5..
1f2c4..
e36e8..
)
e36e8..
Definition
9888f..
:=
λ x0 :
ι →
ι → ο
.
and
(
d6106..
x0
)
(
x0
27862..
1b59f..
)
Conjecture
fa148..
:
∀ x0 x1 :
ι →
ι → ο
.
d6106..
x0
⟶
bb8e6..
x1
⟶
d478c..
x0
x1
1b59f..
Definition
3cd3c..
:=
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
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
x0
)
(
prim0
x1
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
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
x1
x0
)
)
(
prim0
(
prim0
x0
x0
)
(
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
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x0
)
)
(
prim0
(
prim0
x1
x1
)
(
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
)
)
)
)
)
(
prim1
(
λ x0 .
x0
)
)
)
)
)
)
)
)
)
)
Param
57d6a..
:
ι
→
ι
→
ι
Definition
68b13..
:=
91fd5..
(
57d6a..
67794..
5b8fe..
)
32d20..
Definition
3cabe..
:=
λ x0 :
ι →
ι → ο
.
and
(
9888f..
x0
)
(
x0
3cd3c..
68b13..
)
Conjecture
57580..
:
∀ x0 x1 :
ι →
ι → ο
.
9888f..
x0
⟶
bb8e6..
x1
⟶
d478c..
x0
x1
68b13..
Definition
f3baa..
:=
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
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
x0
)
(
prim0
x1
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
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
x1
x0
)
)
(
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
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
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x1
x1
)
)
)
)
)
(
prim1
(
λ x0 .
x0
)
)
)
)
)
)
)
)
)
)
)
Definition
af815..
:=
91fd5..
(
57d6a..
67794..
5b8fe..
)
(
91fd5..
(
57d6a..
67794..
5b8fe..
)
(
57d6a..
67794..
5b8fe..
)
)
Definition
8cc3c..
:=
λ x0 :
ι →
ι → ο
.
and
(
3cabe..
x0
)
(
x0
f3baa..
af815..
)
Conjecture
4ef9d..
:
∀ x0 x1 :
ι →
ι → ο
.
3cabe..
x0
⟶
bb8e6..
x1
⟶
d478c..
x0
x1
af815..
Definition
7a0ec..
:=
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
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
x0
)
(
prim0
x1
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
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
x1
x0
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
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
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
)
)
)
)
)
(
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
x1
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x1
x1
)
)
)
)
)
(
prim1
(
λ x0 .
x0
)
)
)
)
)
)
)
)
)
)
)
)
)
Param
d7cf0..
:
ι
→
(
ι
→
ι
) →
ι
Definition
99fb9..
:=
d7cf0..
1f2c4..
(
λ x0 .
91fd5..
(
91fd5..
(
57d6a..
67794..
x0
)
(
57d6a..
67794..
5b8fe..
)
)
(
57d6a..
67794..
5b8fe..
)
)
Definition
7afff..
:=
λ x0 :
ι →
ι → ο
.
and
(
8cc3c..
x0
)
(
x0
7a0ec..
99fb9..
)
Conjecture
26e08..
:
∀ x0 x1 :
ι →
ι → ο
.
8cc3c..
x0
⟶
bb8e6..
x1
⟶
d478c..
x0
x1
99fb9..
Definition
cb931..
:=
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
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
x0
)
(
prim0
x1
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
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
x1
x0
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x0
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
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
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
)
)
)
)
)
(
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
x1
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x1
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x1
x0
)
)
(
prim0
(
prim0
x1
x1
)
(
prim0
x1
x1
)
)
)
)
)
(
prim1
(
λ x0 .
x0
)
)
)
)
)
)
)
)
)
)
)
)
)
)
Definition
657ef..
:=
91fd5..
(
91fd5..
1f2c4..
(
57d6a..
67794..
5b8fe..
)
)
(
57d6a..
67794..
5b8fe..
)
Definition
d9462..
:=
λ x0 :
ι →
ι → ο
.
and
(
7afff..
x0
)
(
x0
cb931..
657ef..
)
Conjecture
64c5c..
:
∀ x0 x1 :
ι →
ι → ο
.
7afff..
x0
⟶
bb8e6..
x1
⟶
d478c..
x0
x1
657ef..
Param
bcddf..
:
ι
→
(
ι
→
ι
) →
ι
Param
236c6..
:
ι
Definition
e8415..
:=
λ x0 :
ι →
ι → ο
.
and
(
bb8e6..
x0
)
(
x0
67794..
(
bcddf..
236c6..
(
λ x1 .
57d6a..
67ee8..
(
57d6a..
25ca3..
x1
)
)
)
)
Definition
9315d..
:=
λ x0 :
ι →
ι → ο
.
and
(
e8415..
x0
)
(
∀ x1 x2 .
x0
(
57d6a..
67ee8..
(
57d6a..
25ca3..
(
57d6a..
(
57d6a..
62f06..
x1
)
x2
)
)
)
(
91fd5..
(
57d6a..
67794..
x1
)
(
57d6a..
67794..
x2
)
)
)
Definition
77d26..
:=
λ x0 :
ι →
ι → ο
.
and
(
9315d..
x0
)
(
∀ x1 .
x0
(
57d6a..
67ee8..
(
57d6a..
27862..
x1
)
)
(
d7cf0..
1f2c4..
(
λ x2 .
57d6a..
67ee8..
(
57d6a..
x1
x2
)
)
)
)
Definition
9d73b..
:=
λ x0 :
ι →
ι → ο
.
and
(
77d26..
x0
)
(
∀ x1 x2 .
x0
(
57d6a..
3cd3c..
(
57d6a..
(
57d6a..
7a0ec..
x1
)
x2
)
)
(
d7cf0..
(
57d6a..
67794..
x1
)
(
λ x3 .
57d6a..
3cd3c..
(
57d6a..
x2
x3
)
)
)
)
Definition
b531a..
:=
λ x0 :
ι →
ι → ο
.
and
(
9d73b..
x0
)
(
∀ x1 x2 .
x0
(
57d6a..
3cd3c..
(
57d6a..
(
57d6a..
f3baa..
x1
)
x2
)
)
(
91fd5..
(
57d6a..
3cd3c..
x1
)
(
57d6a..
3cd3c..
x2
)
)
)
Definition
bd9b5..
:=
λ x0 :
ι →
ι → ο
.
and
(
b531a..
x0
)
(
∀ x1 .
x0
(
57d6a..
3cd3c..
(
57d6a..
cb931..
x1
)
)
(
d7cf0..
1f2c4..
(
λ x2 .
57d6a..
3cd3c..
(
57d6a..
x1
x2
)
)
)
)
Definition
5bcaf..
:=
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
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
x0
)
(
prim0
x1
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
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
x1
x0
)
)
(
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
x1
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
x0
x1
)
(
prim0
x1
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x1
x1
)
(
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
x0
x1
)
(
prim0
x1
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x0
)
)
(
prim0
(
prim0
x0
x1
)
(
prim0
x0
x1
)
)
)
)
)
(
prim1
(
λ x0 .
x0
)
)
)
)
)
)
)
)
)
)
)
)
)
)
Definition
472f9..
:=
57d6a..
67ee8..
(
57d6a..
27862..
(
bcddf..
1f2c4..
(
λ x0 .
57d6a..
25ca3..
(
57d6a..
(
57d6a..
62f06..
x0
)
(
57d6a..
(
57d6a..
62f06..
x0
)
5b8fe..
)
)
)
)
)
Definition
e0314..
:=
bcddf..
1f2c4..
(
λ x0 .
bcddf..
(
57d6a..
67794..
x0
)
(
λ x1 .
bcddf..
(
57d6a..
67794..
x0
)
(
λ x2 .
57d6a..
(
57d6a..
7a0ec..
(
57d6a..
(
57d6a..
62f06..
x0
)
5b8fe..
)
)
(
bcddf..
236c6..
(
λ x3 .
57d6a..
(
57d6a..
f3baa..
(
57d6a..
x3
x1
)
)
(
57d6a..
x3
x2
)
)
)
)
)
)
Definition
39d15..
:=
λ x0 :
ι →
ι → ο
.
and
(
d9462..
x0
)
(
x0
5bcaf..
472f9..
)
Conjecture
235b5..
:
∀ x0 x1 :
ι →
ι → ο
.
d9462..
x0
⟶
bd9b5..
x1
⟶
d478c..
x0
x1
472f9..
Param
6fe8d..
:
(
ι
→
ι
→
ο
) →
(
ι
→
ι
→
ο
) →
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ο
Param
5c39b..
:
ι
→
ι
→
ο
Conjecture
d3a4f..
:
∀ x0 x1 :
ι →
ι → ο
.
d9462..
x0
⟶
bd9b5..
x1
⟶
6fe8d..
x0
x1
5c39b..
e0314..
472f9..
Definition
9da57..
:=
λ x0 :
ι →
ι → ο
.
and
(
bd9b5..
x0
)
(
x0
5bcaf..
e0314..
)
Definition
63f8a..
:=
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
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
x0
)
(
prim0
x1
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
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
x1
x0
)
)
(
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
)
)
)
)
)
(
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
x0
)
(
prim0
x0
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x0
x0
)
(
prim0
x1
x1
)
)
)
)
)
(
prim1
(
λ x0 .
x0
)
)
)
)
)
)
)
)
)
)
)
Definition
7e7e4..
:=
57d6a..
3cd3c..
(
57d6a..
cb931..
(
bcddf..
236c6..
(
λ x0 .
57d6a..
(
57d6a..
7a0ec..
x0
)
(
bcddf..
(
57d6a..
67794..
x0
)
(
λ x1 .
57d6a..
(
57d6a..
(
57d6a..
5bcaf..
x0
)
x1
)
x1
)
)
)
)
)
Definition
ed937..
:=
bcddf..
1f2c4..
(
λ x0 .
bcddf..
(
57d6a..
67794..
x0
)
(
λ x1 .
bcddf..
(
57d6a..
67794..
(
57d6a..
(
57d6a..
62f06..
x0
)
5b8fe..
)
)
(
λ x2 .
bcddf..
(
57d6a..
3cd3c..
(
57d6a..
x2
x1
)
)
(
λ x3 .
x3
)
)
)
)
Definition
5920d..
:=
λ x0 :
ι →
ι → ο
.
and
(
39d15..
x0
)
(
x0
63f8a..
7e7e4..
)
Conjecture
4daf7..
:
∀ x0 x1 :
ι →
ι → ο
.
39d15..
x0
⟶
9da57..
x1
⟶
d478c..
x0
x1
7e7e4..
Conjecture
ad088..
:
∀ x0 x1 :
ι →
ι → ο
.
39d15..
x0
⟶
9da57..
x1
⟶
6fe8d..
x0
x1
5c39b..
ed937..
7e7e4..
Definition
29aed..
:=
λ x0 :
ι →
ι → ο
.
and
(
9da57..
x0
)
(
x0
63f8a..
ed937..
)
Definition
de260..
:=
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
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
x0
)
(
prim0
x1
x1
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
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
x1
x0
)
)
(
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
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x0
)
)
(
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
x1
x0
)
)
(
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
x1
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
x0
x1
)
(
prim0
x1
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x1
)
)
(
prim0
(
prim0
x1
x1
)
(
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
x0
x1
)
(
prim0
x1
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
(
prim0
x0
x0
)
)
(
prim0
(
prim0
x0
x1
)
(
prim0
x0
x1
)
)
)
)
)
(
prim1
(
λ x0 .
x0
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
Definition
21cd8..
:=
57d6a..
3cd3c..
(
57d6a..
cb931..
(
bcddf..
1f2c4..
(
λ x0 .
57d6a..
(
57d6a..
7a0ec..
x0
)
(
bcddf..
(
57d6a..
67794..
x0
)
(
λ x1 .
57d6a..
(
57d6a..
7a0ec..
x0
)
(
bcddf..
(
57d6a..
67794..
x0
)
(
λ x2 .
57d6a..
(
57d6a..
f3baa..
(
57d6a..
(
57d6a..
(
57d6a..
5bcaf..
x0
)
x1
)
x2
)
)
(
57d6a..
(
57d6a..
(
57d6a..
5bcaf..
x0
)
x2
)
x1
)
)
)
)
)
)
)
)
Definition
5d0c6..
:=
λ x0 :
ι →
ι → ο
.
and
(
5920d..
x0
)
(
x0
de260..
21cd8..
)
Conjecture
fcb0d..
:
∀ x0 x1 :
ι →
ι → ο
.
5920d..
x0
⟶
29aed..
x1
⟶
d478c..
x0
x1
21cd8..
Definition
5d0c6..
:=
5d0c6..
Definition
29aed..
:=
29aed..