Let x0 of type ι be given.
Apply H0 with
λ x1 . x1 = 96158.. (f482f.. x1 4a7ef..) (e3162.. (f482f.. x1 (4ae4a.. 4a7ef..))) (f482f.. x1 (4ae4a.. (4ae4a.. 4a7ef..))).
Let x1 of type ι be given.
Let x2 of type ι → ι → ι be given.
Let x3 of type ι be given.
Apply unknownprop_3bd6f6e5afa239de2bed4c5d0a7e768286a329bd2689d74ed28c7c62d231db6f with
x1,
x2,
x3,
λ x4 x5 . 96158.. x1 x2 x3 = 96158.. x4 (e3162.. (f482f.. (96158.. x1 x2 x3) (4ae4a.. 4a7ef..))) (f482f.. (96158.. x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..))).
Apply unknownprop_22fa583cdd675dc491864c4bc88d6afb2cb2c5c899f3088bafeb1dd37fbf3527 with
x1,
x2,
x3,
λ x4 x5 . 96158.. x1 x2 x3 = 96158.. x1 (e3162.. (f482f.. (96158.. x1 x2 x3) (4ae4a.. 4a7ef..))) x4.
Apply unknownprop_ba0ccf72f15c7ded5ee2dcc20bbf84c6b9467eb3d05b62ae3fe68c2fa7163efe with
x1,
x2,
e3162.. (f482f.. (96158.. x1 x2 x3) (4ae4a.. 4a7ef..)),
x3.
The subproof is completed by applying unknownprop_aec86eb4da68e7f79235ce435d2568a1f89bad923e23fefb04b9885bd4542138 with x1, x2, x3.