Let x0 of type ι be given.
Apply H0 with
λ x1 . x1 = 5fdf5.. (f482f.. x1 4a7ef..) (f482f.. (f482f.. x1 (4ae4a.. 4a7ef..))) (f482f.. (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 → ι be given.
Apply unknownprop_543686e66106ef7fd22156a4009f0d2a9db2343f2534c11212b55b0c2e92283e with
x1,
x2,
x3,
λ x4 x5 . 5fdf5.. x1 x2 x3 = 5fdf5.. x4 (f482f.. (f482f.. (5fdf5.. x1 x2 x3) (4ae4a.. 4a7ef..))) (f482f.. (f482f.. (5fdf5.. x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..)))).
Apply unknownprop_5ca5a876de766128cd181224f0e183a55c30303f3e6f0e43887843a99a96a2b1 with
x1,
x2,
f482f.. (f482f.. (5fdf5.. x1 x2 x3) (4ae4a.. 4a7ef..)),
x3,
f482f.. (f482f.. (5fdf5.. x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..))) leaving 2 subgoals.
The subproof is completed by applying unknownprop_cbe3477448d585dc62b5597e422b06d1afa24a5af2e7522929e0b9389e0afec8 with x1, x2, x3.
The subproof is completed by applying unknownprop_952db7193be9ed6add7b4388af9a31411f1f39400c1e751d83d30221f79965d8 with x1, x2, x3.