Let x0 of type ι be given.
Apply H0 with
λ x1 . x1 = 08354.. (f482f.. x1 4a7ef..) (2b2e3.. (f482f.. x1 (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. x1 (4ae4a.. (4ae4a.. 4a7ef..)))).
Let x1 of type ι be given.
Let x2 of type ι → ι → ο be given.
Let x3 of type ι → ι → ο be given.
Apply unknownprop_ba8500d70b6837e6ba201d4cb6447659635fe1e1465284d8fdf0e1c9742304e8 with
x1,
x2,
x3,
λ x4 x5 . 08354.. x1 x2 x3 = 08354.. x4 (2b2e3.. (f482f.. (08354.. x1 x2 x3) (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. (08354.. x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..)))).
Apply unknownprop_40fe051c0dc0ea3ed4cccc5ed1eff06af0bed8e9e13e56c19f3d0fb77b6ab461 with
x1,
x2,
2b2e3.. (f482f.. (08354.. x1 x2 x3) (4ae4a.. 4a7ef..)),
x3,
2b2e3.. (f482f.. (08354.. x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..))) leaving 2 subgoals.
Let x4 of type ι be given.
Let x5 of type ι be given.
Apply unknownprop_e73c46d626b1cba3a6b1ae73b9993b5fe8c340292b205804e43b4aa3b7e892f6 with
x1,
x2,
x3,
x4,
x5,
λ x6 x7 : ο . iff (x2 x4 x5) x6 leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying iff_refl with x2 x4 x5.
Let x4 of type ι be given.
Let x5 of type ι be given.
Apply unknownprop_a80b211237ab702683e3180bd24e2b20952c0f34a890418d470413fac50be678 with
x1,
x2,
x3,
x4,
x5,
λ x6 x7 : ο . iff (x3 x4 x5) x6 leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying iff_refl with x3 x4 x5.