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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:
3e00e..
x0
x1
=
3e00e..
x2
x3
.
Apply unknownprop_f4ff16b9b21fb43bec0dd0d2e94569d632f3d21b75932b9bcc0c1ffd4c0d62b6 with
x0
,
x1
,
x2
,
x3
.
Apply unknownprop_3b55668ebff4b5090f31d28781617fd36508e9eaa3458c4a604deaa4db096497 with
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
...
)
)
)
)
)
...
)
)
)
)
)
)
)
)
)
)
)
,
...
,
...
,
...
.
...
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