Let x0 of type ι be given.
Apply H0 with
λ x1 . x1 = 81367.. (f482f.. x1 4a7ef..) (f482f.. (f482f.. x1 (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. x1 (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. x1 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))).
Let x1 of type ι be given.
Let x2 of type ι → ι be given.
Let x3 of type ι → ι → ο be given.
Let x4 of type ι → ο be given.
Apply unknownprop_b420ee51d5d19ad980a4810713a3ef2428660a173fc05982fad8090ea4d95bd4 with
x1,
x2,
x3,
x4,
λ x5 x6 . 81367.. x1 x2 x3 x4 = 81367.. x5 (f482f.. (f482f.. (81367.. x1 x2 x3 x4) (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. (81367.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. (81367.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))).
Apply unknownprop_f15cb07fa8940f8ed7d9661e8cedae2d309059b4f036a189fe365a29976c0ccc with
x1,
x2,
f482f.. (f482f.. (81367.. x1 x2 x3 x4) (4ae4a.. 4a7ef..)),
x3,
2b2e3.. (f482f.. (81367.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))),
x4,
decode_p (f482f.. (81367.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) leaving 3 subgoals.
The subproof is completed by applying unknownprop_8adc62668ab8010ee4cf20ab2423c96fa058b125068a120ed3f4ac00a4a48e1d with x1, x2, x3, x4.
Let x5 of type ι be given.
Let x6 of type ι be given.
Apply unknownprop_2e831d5836c0f35ebf271acc4aaeb289f7e5a8e725e8249195a6239140317c54 with
x1,
x2,
x3,
x4,
x5,
x6,
λ x7 x8 : ο . iff (x3 x5 x6) x7 leaving 3 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying iff_refl with x3 x5 x6.
Let x5 of type ι be given.
Apply unknownprop_29ad1a240e68bbe865919b85594b1639c5129575d9e47f21dcb92a9681f803d2 with
x1,
x2,
x3,
x4,
x5,
λ x6 x7 : ο . iff (x4 x5) x6 leaving 2 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying iff_refl with x4 x5.