Let x0 of type ι be given.
Let x1 of type ι be given.
Apply unknownprop_b456609235d152f08bccfce314d541d7c44f3716137c00b0ce21cf467ba83d17 with
4ae4a.. (4ae4a.. 4a7ef..),
λ x2 . If_i (x2 = 4a7ef..) x0 x1,
4a7ef..,
λ x2 x3 . x3 = x0 leaving 2 subgoals.
The subproof is completed by applying unknownprop_94c438c3f41134cd86e0be06a85b5e5b3aa8448f9221f51d2dfe9b1364042f49.
Apply If_i_1 with
4a7ef.. = 4a7ef..,
x0,
x1.
Let x2 of type ι → ι → ο be given.
The subproof is completed by applying H0.