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.

Apply unknownprop_b456609235d152f08bccfce314d541d7c44f3716137c00b0ce21cf467ba83d17 with 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))), λ x4 . If_i (x4 = 4a7ef..) x0 (If_i (x4 = 4ae4a.. 4a7ef..) x1 (If_i (x4 = 4ae4a.. (4ae4a.. 4a7ef..)) x2 x3)), 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)), λ x4 x5 . x5 = x3 leaving 2 subgoals.

The subproof is completed by applying unknownprop_24c97a952f8399b0fe8a6a3b53b4d452db6969b6becdddf85e0cb080a983a491.

The subproof is completed by applying unknownprop_39c68f59201a24e05d494df554b752ed6bfbdb14109c09811c3da46652b4b359.

Apply If_i_0 with 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)) = 4ae4a.. 4a7ef.., x1, If_i (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)) = 4ae4a.. (4ae4a.. 4a7ef..)) x2 x3, λ x4 x5 . x5 = x3 leaving 2 subgoals.

The subproof is completed by applying unknownprop_660d518b3f18494e3056984097a0917e4ddb34b7d7ca0e50c6808ad2c4676ba8.

The subproof is completed by applying unknownprop_73033d4e951667af4b4a387afc6dabb25c26071ba21f7aaa1e5a3c5c21a42316.

■

Proofgold Proof