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Proofgold Proof
pf
Let x0 of type
ι
be given.
Let x1 of type
ι
be given.
The subproof is completed by applying unknownprop_47684d77daf9976982fef9cd65f54cb0f256a9046ee087c4a3bf5f6bf45def6c with
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
x3
x2
)
(
prim0
x2
x3
)
)
(
prim0
(
prim0
x2
x3
)
(
prim0
x3
x2
)
)
)
)
)
(
prim0
(
prim1
(
λ x2 .
prim1
(
λ x3 .
prim0
(
prim0
(
prim0
x3
x2
)
...
)
...
)
)
)
...
)
)
)
)
)
)
)
)
)
)
)
)
,
...
,
...
.
■