Let x0 of type ι be given.
Apply H0 with
λ x1 . x1 = 8eacd.. (f482f.. x1 4a7ef..) (f482f.. (f482f.. x1 (4ae4a.. 4a7ef..))) (f482f.. x1 (4ae4a.. (4ae4a.. 4a7ef..))).
Let x1 of type ι be given.
Let x2 of type ι → ι be given.
Let x3 of type ι be given.
Apply unknownprop_128401b26ca0bc08d54bfca9904ebdbf186db1274a4be846be9a9cc30eb990c9 with
x1,
x2,
x3,
λ x4 x5 . 8eacd.. x1 x2 x3 = 8eacd.. x4 (f482f.. (f482f.. (8eacd.. x1 x2 x3) (4ae4a.. 4a7ef..))) (f482f.. (8eacd.. x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..))).
Apply unknownprop_e852dd30a45cb3a8cce74800ccca965088221e00f4794a6d5a0a5270b65d5a2a with
x1,
x2,
x3,
λ x4 x5 . 8eacd.. x1 x2 x3 = 8eacd.. x1 (f482f.. (f482f.. (8eacd.. x1 x2 x3) (4ae4a.. 4a7ef..))) x4.
Apply unknownprop_31e0846896c60dc9a369a32236037cd02bc5bb14f565f447189cc52ef6a737da with
x1,
x2,
f482f.. (f482f.. (8eacd.. x1 x2 x3) (4ae4a.. 4a7ef..)),
x3.
The subproof is completed by applying unknownprop_185dfaf856c8b7f2b4591a434b0b04e8904e3e58c14681f42a4c6a9bacc9a6c3 with x1, x2, x3.