Let x0 of type ι be given.
Apply H0 with
λ x1 . x1 = 33a0d.. (f482f.. x1 4a7ef..) (e3162.. (f482f.. x1 (4ae4a.. 4a7ef..))) (decode_p (f482f.. x1 (4ae4a.. (4ae4a.. 4a7ef..)))).
Let x1 of type ι be given.
Let x2 of type ι → ι → ι be given.
Let x3 of type ι → ο be given.
Apply unknownprop_9fa32bd638e8c31d6b182a5633791e799b87de2a4ba474c8268d6be18d528c69 with
x1,
x2,
x3,
λ x4 x5 . 33a0d.. x1 x2 x3 = 33a0d.. x4 (e3162.. (f482f.. (33a0d.. x1 x2 x3) (4ae4a.. 4a7ef..))) (decode_p (f482f.. (33a0d.. x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..)))).
Apply unknownprop_dfc2fc71cc6e6a486a193bcd99dbcfa97487476c6e7b2c2d0dd4109dd2851142 with
x1,
x2,
e3162.. (f482f.. (33a0d.. x1 x2 x3) (4ae4a.. 4a7ef..)),
x3,
decode_p (f482f.. (33a0d.. x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..))) leaving 2 subgoals.
The subproof is completed by applying unknownprop_4e0a023e0994003d0aeb1b6b3ffa0ab2be65253744ded6ca621dc0f96c465796 with x1, x2, x3.
Let x4 of type ι be given.
Apply unknownprop_fd2efe54fe67f3ab31cabede3eaf251effecfe7cd1887072248950b21a2f3196 with
x1,
x2,
x3,
x4,
λ x5 x6 : ο . iff (x3 x4) x5 leaving 2 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying iff_refl with x3 x4.