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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.
Apply unknownprop_b456609235d152f08bccfce314d541d7c44f3716137c00b0ce21cf467ba83d17 with
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
)
,
λ x6 .
If_i
(
x6
=
4a7ef..
)
x0
(
If_i
(
x6
=
4ae4a..
4a7ef..
)
x1
(
If_i
(
x6
=
4ae4a..
(
4ae4a..
4a7ef..
)
)
x2
(
If_i
(
x6
=
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
x3
(
If_i
(
x6
=
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
x4
x5
)
)
)
)
,
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
,
λ x6 x7 .
x7
=
x5
leaving 2 subgoals.
The subproof is completed by applying unknownprop_c2c69282b56a7886253ce9f1e28af8e349fa495f30f9b9692bd8b0ec32e94b88.
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
x5
)
)
)
,
λ x6 x7 .
x7
=
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
x5
)
)
,
λ x6 x7 .
x7
=
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
x5
)
,
λ x6 x7 .
x7
=
x5
leaving 2 subgoals.
The subproof is completed by applying unknownprop_9cfee97ab21e62e15620e85434010a51b920daf40f28c85a8dc692e552bd3196.
Apply If_i_0 with
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
x5
,
λ x6 x7 .
x7
=
x5
leaving 2 subgoals.
The subproof is completed by applying unknownprop_c426ab567a5c5ab365eacf0441778a76adba2025b094fe331959e46984d6ecd9.
Apply If_i_0 with
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
)
=
4ae4a..
(
4ae4a..
(
4ae4a..
(
4ae4a..
4a7ef..
)
)
)
,
x4
,
x5
.
The subproof is completed by applying unknownprop_1a1d3efda6a05c42a5fac3f44809fe1fbdff438b32e409d6c0b0af7a66c07f88.
■