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Proofgold Proof
pf
Let x0 of type
ι
be given.
Let x1 of type
ι
be given.
Let x2 of type
ι
be given.
Let x3 of type
ι
be given.
Assume H0:
prim0
(
prim0
(
prim1
(
λ x4 .
prim1
(
λ x5 .
prim0
(
prim0
(
prim0
x5
x4
)
(
prim0
x4
x5
)
)
(
prim0
(
prim0
x5
x5
)
(
prim0
x4
x4
)
)
)
)
)
(
prim0
(
prim1
(
λ x4 .
prim1
(
λ x5 .
prim0
(
prim0
(
prim0
x5
x4
)
(
prim0
x4
x5
)
)
(
prim0
(
prim0
x4
x4
)
(
prim0
x4
x4
)
)
)
)
)
(
prim0
(
prim1
(
λ x4 .
prim1
(
λ x5 .
prim0
(
prim0
(
prim0
x5
x4
)
(
prim0
x4
x4
)
)
(
prim0
(
prim0
x5
x5
)
(
prim0
x4
x5
)
)
)
)
)
(
prim0
(
prim1
(
λ x4 .
prim1
(
λ x5 .
prim0
(
prim0
(
prim0
x5
x4
)
(
prim0
x4
x5
)
)
(
prim0
(
prim0
x5
x4
)
(
prim0
x5
x4
)
)
)
)
)
(
prim0
(
prim1
(
λ x4 .
prim1
(
λ x5 .
prim0
(
prim0
(
prim0
x5
x4
)
(
prim0
x5
x4
)
)
(
prim0
(
prim0
x4
x4
)
(
prim0
x4
x4
)
)
)
)
)
(
prim0
(
prim1
(
λ x4 .
prim1
(
λ x5 .
prim0
(
prim0
(
prim0
x5
x4
)
(
prim0
x4
x4
)
)
(
prim0
(
prim0
x5
x5
)
(
prim0
x4
x4
)
)
)
)
)
(
prim0
(
prim1
(
λ x4 .
prim1
(
λ x5 .
prim0
(
prim0
(
prim0
x5
x4
)
(
prim0
x4
x5
)
)
(
prim0
(
prim0
x4
x5
)
(
prim0
x5
x4
)
)
)
)
)
(
prim0
(
prim1
(
λ x4 .
prim1
(
λ x5 .
prim0
(
prim0
(
prim0
x5
x4
)
(
prim0
x4
x5
)
)
(
prim0
(
prim0
x4
x4
)
(
prim0
x5
x4
)
)
)
)
)
(
prim0
(
prim1
(
λ x4 .
prim1
(
λ x5 .
prim0
(
prim0
(
prim0
x5
x4
)
(
prim0
x4
x4
)
)
(
prim0
(
prim0
x5
x5
)
(
prim0
x5
x5
)
)
)
)
)
(
prim0
(
prim1
(
λ x4 .
prim1
(
λ x5 .
prim0
(
prim0
(
prim0
x5
x4
)
(
prim0
x4
x5
)
)
(
prim0
(
prim0
x4
x4
)
(
prim0
x5
x5
)
)
)
)
)
(
prim0
(
prim1
(
λ x4 .
prim1
(
λ x5 .
prim0
(
prim0
(
prim0
x5
x4
)
(
prim0
x4
x5
)
)
(
prim0
(
prim0
x4
x5
)
(
prim0
x5
x4
)
)
)
)
)
(
prim0
(
prim1
(
λ x4 .
prim1
(
λ x5 .
prim0
(
prim0
(
prim0
x5
x4
)
(
prim0
x4
x5
)
)
(
prim0
(
prim0
x5
x5
)
(
prim0
x4
x4
)
)
)
)
)
(
prim0
(
prim1
(
λ x4 .
prim1
(
λ x5 .
prim0
(
prim0
...
...
)
...
)
)
)
...
)
)
)
)
)
)
)
)
)
)
)
)
)
...
=
...
.
...
■