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