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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.
Let x5 of type
ι
be given.
Let x6 of type
ι
be given.
Apply unknownprop_b456609235d152f08bccfce314d541d7c44f3716137c00b0ce21cf467ba83d17 with
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
)
)
,
λ x7 .
If_i
(
x7
=
4a7ef..
)
x0
(
If_i
(
x7
=
4ae4a..
4a7ef..
)
x1
(
If_i
(
x7
=
4ae4a..
(
4ae4a..
4a7ef..
)
)
x2
(
If_i
(
x7
=
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
x3
(
If_i
(
x7
=
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
x4
(
If_i
(
x7
=
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
)
x5
x6
)
)
)
)
)
,
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
,
λ x7 x8 .
x8
=
x5
leaving 2 subgoals.
The subproof is completed by applying unknownprop_e8aa0dbc3c114f21a34c7abfd83b16dc66ff0243be985c8ee2f8ef5bc459f676.
Apply If_i_0 with
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
=
4a7ef..
,
x0
,
If_i
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
=
4ae4a..
4a7ef..
)
x1
(
If_i
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
=
4ae4a..
(
4ae4a..
4a7ef..
)
)
x2
(
If_i
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
=
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
x3
(
If_i
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
=
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
x4
(
If_i
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
=
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
)
x5
x6
)
)
)
)
,
λ x7 x8 .
x8
=
x5
leaving 2 subgoals.
The subproof is completed by applying unknownprop_a28806a210b61567a3ab53c41670dd2cdd0954582f81581ebc35a00116effb38.
Apply If_i_0 with
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
=
4ae4a..
4a7ef..
,
x1
,
If_i
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
=
4ae4a..
(
4ae4a..
4a7ef..
)
)
x2
(
If_i
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
=
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
x3
(
If_i
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
=
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
x4
(
If_i
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
=
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
)
x5
x6
)
)
)
,
λ x7 x8 .
x8
=
x5
leaving 2 subgoals.
The subproof is completed by applying unknownprop_277d6d7121479b5a4376f24b0cde62a343397396992f54847fcdd9c228b6775f.
Apply If_i_0 with
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
=
4ae4a..
(
4ae4a..
4a7ef..
)
,
x2
,
If_i
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
=
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
x3
(
If_i
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
=
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
x4
(
If_i
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
=
4ae4a..
(
4ae4a..
(
4ae4a..
...
)
)
)
...
...
)
)
,
...
leaving 2 subgoals.
...
...
■