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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.
Let x4 of type
ι
be given.
Apply unknownprop_b456609235d152f08bccfce314d541d7c44f3716137c00b0ce21cf467ba83d17 with
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
,
λ x5 .
If_i
(
x5
=
4a7ef..
)
x0
(
If_i
(
x5
=
4ae4a..
4a7ef..
)
x1
(
If_i
(
x5
=
4ae4a..
(
4ae4a..
4a7ef..
)
)
x2
(
If_i
(
x5
=
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
x3
x4
)
)
)
,
4a7ef..
,
λ x5 x6 .
x6
=
x0
leaving 2 subgoals.
The subproof is completed by applying unknownprop_65971d7fb82cf658cabe1adc2decc738c44e6424e0df2d626e88c5c4d2ad7ccb.
Apply If_i_1 with
4a7ef..
=
4a7ef..
,
x0
,
If_i
(
4a7ef..
=
4ae4a..
4a7ef..
)
x1
(
If_i
(
4a7ef..
=
4ae4a..
(
4ae4a..
4a7ef..
)
)
x2
(
If_i
(
4a7ef..
=
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
x3
x4
)
)
.
Let x5 of type
ι
→
ι
→
ο
be given.
Assume H0:
x5
4a7ef..
4a7ef..
.
The subproof is completed by applying H0.
■