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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.
Apply unknownprop_b456609235d152f08bccfce314d541d7c44f3716137c00b0ce21cf467ba83d17 with
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
)
)
)
,
λ x8 .
If_i
(
x8
=
4a7ef..
)
x0
(
If_i
(
x8
=
4ae4a..
4a7ef..
)
x1
(
If_i
(
x8
=
4ae4a..
(
4ae4a..
4a7ef..
)
)
x2
(
If_i
(
x8
=
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
x3
(
If_i
(
x8
=
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
x4
(
If_i
(
x8
=
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
)
x5
(
If_i
(
x8
=
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
)
)
x6
x7
)
)
)
)
)
)
,
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
,
λ x8 x9 .
x9
=
x4
leaving 2 subgoals.
The subproof is completed by applying unknownprop_4eb37da7295db004b560655a73d423507c088c54f945c8a3c59fd95ac4fa8b33.
Apply If_i_0 with
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
=
4a7ef..
,
x0
,
If_i
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
=
4ae4a..
4a7ef..
)
x1
(
If_i
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
=
4ae4a..
(
4ae4a..
4a7ef..
)
)
x2
(
If_i
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
=
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
x3
(
If_i
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
=
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
x4
(
If_i
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
=
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
)
x5
(
If_i
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
=
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
)
)
x6
x7
)
)
)
)
)
,
λ x8 x9 .
x9
=
x4
leaving 2 subgoals.
The subproof is completed by applying unknownprop_ad3d8dc286672dabbf45d75a5bddff9246ae99a1b47ead9979d5568de89957bd.
Apply If_i_0 with
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
=
4ae4a..
4a7ef..
,
x1
,
If_i
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
=
4ae4a..
(
4ae4a..
4a7ef..
)
)
x2
(
If_i
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
=
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
x3
(
If_i
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
=
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
x4
(
If_i
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
=
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
)
x5
(
If_i
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
=
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
)
)
x6
x7
)
)
)
)
,
λ x8 x9 .
x9
=
x4
leaving 2 subgoals.
The subproof is completed by applying unknownprop_ac927f2ad247eb36bc322e3579f4429fc5e423f90a2de7867227e2cfdd51eb3e.
Apply If_i_0 with
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
=
4ae4a..
(
4ae4a..
4a7ef..
)
,
x2
,
If_i
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
=
4ae4a..
(
4ae4a..
...
)
)
...
...
,
...
leaving 2 subgoals.
...
...
■