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Proofgold Proof
pf
Assume H0:
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
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
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
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
)
)
)
)
)
(
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
x0
)
)
)
)
)
(
prim0
(
prim1
(
λ x0 .
prim1
(
λ x1 .
prim0
(
prim0
(
prim0
x1
x0
)
...
)
...
)
)
)
...
)
)
)
)
)
)
)
)
)
)
)
)
=
...
.
...
■