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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:
equip
(
setsum
(
setsum
(
setprod
x0
(
setprod
(
setexp
x1
50a6b..
)
(
setprod
(
setexp
x2
50a6b..
)
(
setexp
x3
50a6b..
)
)
)
)
(
setsum
(
setprod
x0
(
setprod
(
setexp
x1
50a6b..
)
(
setprod
(
setexp
x2
50a6b..
)
(
setexp
x3
33cc2..
)
)
)
)
(
setsum
(
setprod
x0
(
setprod
(
setexp
x1
50a6b..
)
(
setprod
(
setexp
x2
50a6b..
)
x3
)
)
)
(
setsum
(
setprod
x0
(
setprod
(
setexp
x1
50a6b..
)
(
setexp
x2
50a6b..
)
)
)
(
setsum
(
setprod
x0
(
setprod
(
setexp
x1
50a6b..
)
(
setprod
(
setexp
x2
33cc2..
)
(
setexp
x3
50a6b..
)
)
)
)
(
setsum
(
setprod
x0
(
setprod
(
setexp
x1
50a6b..
)
(
setprod
(
setexp
x2
33cc2..
)
(
setexp
x3
33cc2..
)
)
)
)
(
setsum
(
setprod
x0
(
setprod
(
setexp
x1
50a6b..
)
(
setprod
(
setexp
x2
33cc2..
)
x3
)
)
)
(
setsum
(
setprod
x0
(
setprod
(
setexp
x1
50a6b..
)
(
setexp
x2
33cc2..
)
)
)
(
setsum
(
setprod
x0
(
setprod
(
setexp
x1
50a6b..
)
(
setprod
x2
(
setexp
x3
50a6b..
)
)
)
)
(
setsum
(
setprod
x0
(
setprod
(
setexp
x1
50a6b..
)
(
setprod
x2
(
setexp
x3
33cc2..
)
)
)
)
(
setsum
(
setprod
x0
(
setprod
(
setexp
x1
50a6b..
)
(
setprod
x2
x3
)
)
)
(
setsum
(
setprod
x0
(
setprod
(
setexp
x1
50a6b..
)
x2
)
)
(
setsum
(
setprod
x0
(
setprod
(
setexp
x1
50a6b..
)
(
setexp
x3
50a6b..
)
)
)
(
setsum
(
setprod
x0
(
setprod
(
setexp
x1
50a6b..
)
(
setexp
x3
33cc2..
)
)
)
(
setsum
(
setprod
x0
(
setprod
(
setexp
x1
50a6b..
)
x3
)
)
(
setsum
(
setprod
x0
(
setexp
x1
50a6b..
)
)
(
setsum
(
setprod
x0
(
setprod
(
setexp
x1
33cc2..
)
(
setprod
(
setexp
x2
50a6b..
)
(
setexp
x3
50a6b..
)
)
)
)
(
setsum
(
setprod
x0
(
setprod
(
setexp
x1
33cc2..
)
(
setprod
(
setexp
x2
50a6b..
)
(
setexp
x3
33cc2..
)
)
)
)
(
setsum
(
setprod
x0
(
setprod
(
setexp
x1
33cc2..
)
(
setprod
(
setexp
x2
50a6b..
)
x3
)
)
)
(
setsum
(
setprod
x0
(
setprod
(
setexp
x1
33cc2..
)
(
setexp
x2
50a6b..
)
)
)
(
setsum
(
setprod
x0
(
setprod
(
setexp
x1
33cc2..
)
(
setprod
(
setexp
x2
33cc2..
)
(
setexp
x3
50a6b..
)
)
)
)
(
setsum
(
setprod
x0
(
setprod
(
setexp
x1
...
)
...
)
)
...
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
...
)
...
.
...
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