Let x0 of type ι be given.
Apply H0 with
λ x1 . x1 = 9a89f.. (f482f.. x1 4a7ef..) (decode_p (f482f.. x1 (4ae4a.. 4a7ef..))) (decode_p (f482f.. x1 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x1 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))).
Let x1 of type ι be given.
Let x2 of type ι → ο be given.
Let x3 of type ι → ο be given.
Let x4 of type ι be given.
Apply unknownprop_a576ff427cd318768867456a602be7385ebe63dbd963b27f10917adc75dc8282 with
x1,
x2,
x3,
x4,
λ x5 x6 . 9a89f.. x1 x2 x3 x4 = 9a89f.. x5 (decode_p (f482f.. (9a89f.. x1 x2 x3 x4) (4ae4a.. 4a7ef..))) (decode_p (f482f.. (9a89f.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. (9a89f.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))).
Apply unknownprop_192fd6bdb7e2fbd211637c744c2a289601fd6343dc99fbe58167f21d601083f0 with
x1,
x2,
x3,
x4,
λ x5 x6 . 9a89f.. x1 x2 x3 x4 = 9a89f.. x1 (decode_p (f482f.. (9a89f.. x1 x2 x3 x4) (4ae4a.. 4a7ef..))) (decode_p (f482f.. (9a89f.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..)))) x5.
Apply unknownprop_176b76cb0f2a6cb5f5b2ca0aeeab5816de28188b52b1561f2be2742a173af0f4 with
x1,
x2,
decode_p (f482f.. (9a89f.. x1 x2 x3 x4) (4ae4a.. 4a7ef..)),
x3,
decode_p (f482f.. (9a89f.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))),
x4 leaving 2 subgoals.
Let x5 of type ι be given.
Apply unknownprop_4548e98d35c6fb7e16df7a33511bfb2db06dacdf7d2ed47cd75df680654af064 with
x1,
x2,
x3,
x4,
x5,
λ x6 x7 : ο . iff (x2 x5) x6 leaving 2 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying iff_refl with x2 x5.
Let x5 of type ι be given.
Apply unknownprop_993bd80091dd1d96989c6f7e5192d0c5e7c03a63fa9eb1a1dcfc0ffe8d54833d with
x1,
x2,
x3,
x4,
x5,
λ x6 x7 : ο . iff (x3 x5) x6 leaving 2 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying iff_refl with x3 x5.