Let x0 of type ι be given.
Apply H0 with
λ x1 . x1 = 5f5a0.. (f482f.. x1 4a7ef..) (decode_p (f482f.. x1 (4ae4a.. 4a7ef..))) (f482f.. x1 (4ae4a.. (4ae4a.. 4a7ef..))).
Let x1 of type ι be given.
Let x2 of type ι → ο be given.
Let x3 of type ι be given.
Apply unknownprop_a24d00d7d58489d5e03d60c0e95229905bfc68c6753101dbb87b43d46b7bffe2 with
x1,
x2,
x3,
λ x4 x5 . 5f5a0.. x1 x2 x3 = 5f5a0.. x4 (decode_p (f482f.. (5f5a0.. x1 x2 x3) (4ae4a.. 4a7ef..))) (f482f.. (5f5a0.. x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..))).
Apply unknownprop_e800aee987e9a3dc43bc88979595ea06431689cd684eb2e3aa9b1f10aef3d05c with
x1,
x2,
x3,
λ x4 x5 . 5f5a0.. x1 x2 x3 = 5f5a0.. x1 (decode_p (f482f.. (5f5a0.. x1 x2 x3) (4ae4a.. 4a7ef..))) x4.
Apply unknownprop_82fc62cbb43d5abb2e785b028db9bb1303bc085cb8cc1acd7e60aa88ad3f55af with
x1,
x2,
decode_p (f482f.. (5f5a0.. x1 x2 x3) (4ae4a.. 4a7ef..)),
x3.
Let x4 of type ι be given.
Apply unknownprop_40730fb0a004b91a28776735d67465e69576d851dd9fd3b6f48aaa88954c688b with
x1,
x2,
x3,
x4,
λ x5 x6 : ο . iff (x2 x4) x5 leaving 2 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying iff_refl with x2 x4.