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.. 4a7ef..)), λ x6 x7 . x7 = x3 leaving 2 subgoals.

The subproof is completed by applying unknownprop_8e99f04b9b3449485bc1a33ea56c3d06ecf29ea23e5f1e45f4175a48f7f93ef2.

The subproof is completed by applying unknownprop_39c68f59201a24e05d494df554b752ed6bfbdb14109c09811c3da46652b4b359.

The subproof is completed by applying unknownprop_660d518b3f18494e3056984097a0917e4ddb34b7d7ca0e50c6808ad2c4676ba8.

The subproof is completed by applying unknownprop_73033d4e951667af4b4a387afc6dabb25c26071ba21f7aaa1e5a3c5c21a42316.

Let x6 of type ι → ι → ο be given.

The subproof is completed by applying H0.

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Proofgold Proof