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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.
Let x7 of type
ι
be given.
Let x8 of type
ι
be given.
Apply unknownprop_b456609235d152f08bccfce314d541d7c44f3716137c00b0ce21cf467ba83d17 with
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
)
)
)
)
,
λ x9 .
If_i
(
x9
=
4a7ef..
)
x0
(
If_i
(
x9
=
4ae4a..
4a7ef..
)
x1
(
If_i
(
x9
=
4ae4a..
(
4ae4a..
4a7ef..
)
)
x2
(
If_i
(
x9
=
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
x3
(
If_i
(
x9
=
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
x4
(
If_i
(
x9
=
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
)
x5
(
If_i
(
x9
=
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
)
)
x6
(
If_i
(
x9
=
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
)
)
)
x7
x8
)
)
)
)
)
)
)
,
4ae4a..
(
4ae4a..
4a7ef..
)
,
λ x9 x10 .
x10
=
x2
leaving 2 subgoals.
The subproof is completed by applying unknownprop_f6c183b130f8d109220ce9a1a129e63f813037cf1c26158a7f3f76daed19aefa.
Apply If_i_0 with
4ae4a..
(
4ae4a..
4a7ef..
)
=
4a7ef..
,
x0
,
If_i
(
4ae4a..
(
4ae4a..
4a7ef..
)
=
4ae4a..
4a7ef..
)
x1
(
If_i
(
4ae4a..
(
4ae4a..
4a7ef..
)
=
4ae4a..
(
4ae4a..
4a7ef..
)
)
x2
(
If_i
(
4ae4a..
(
4ae4a..
4a7ef..
)
=
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
x3
(
If_i
(
4ae4a..
(
4ae4a..
4a7ef..
)
=
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
x4
(
If_i
(
4ae4a..
(
4ae4a..
4a7ef..
)
=
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
)
x5
(
If_i
(
4ae4a..
(
4ae4a..
4a7ef..
)
=
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
)
)
x6
(
If_i
(
4ae4a..
(
4ae4a..
4a7ef..
)
=
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
)
)
)
x7
x8
)
)
)
)
)
)
,
λ x9 x10 .
x10
=
x2
leaving 2 subgoals.
The subproof is completed by applying unknownprop_38b5b92bfd131ef0428a8ee212f746419349b56c1e9077ab24b3c25647caace1.
Apply If_i_0 with
4ae4a..
(
4ae4a..
4a7ef..
)
=
4ae4a..
4a7ef..
,
x1
,
If_i
(
4ae4a..
(
4ae4a..
4a7ef..
)
=
4ae4a..
(
4ae4a..
4a7ef..
)
)
x2
(
If_i
(
4ae4a..
(
4ae4a..
4a7ef..
)
=
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
x3
(
If_i
(
4ae4a..
(
4ae4a..
4a7ef..
)
=
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
x4
(
If_i
(
4ae4a..
(
4ae4a..
4a7ef..
)
=
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
)
x5
(
If_i
(
4ae4a..
(
4ae4a..
4a7ef..
)
=
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
)
)
x6
(
If_i
(
4ae4a..
(
4ae4a..
4a7ef..
)
=
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
)
)
)
x7
x8
)
)
)
)
)
,
λ x9 x10 .
x10
=
x2
leaving 2 subgoals.
The subproof is completed by applying unknownprop_e0e602efce8c3fbbb791d74669e968feb76e9d28b29f3878aea98e1fe1efe584.
Apply If_i_1 with
4ae4a..
(
4ae4a..
4a7ef..
)
=
4ae4a..
(
4ae4a..
...
)
,
...
,
...
.
...
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