Let x0 of type ι be given.
Apply H0 with
λ x1 . x1 = 1670d.. (f482f.. x1 4a7ef..) (e3162.. (f482f.. x1 (4ae4a.. 4a7ef..))) (f482f.. (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 → ι be given.
Let x3 of type ι → ι be given.
Let x4 of type ι → ο be given.
Apply unknownprop_671251b916faa9f30bde4669a014519d7c43936df2d92d60762c27df7b65a3f5 with
x1,
x2,
x3,
x4,
λ x5 x6 . 1670d.. x1 x2 x3 x4 = 1670d.. x5 (e3162.. (f482f.. (1670d.. x1 x2 x3 x4) (4ae4a.. 4a7ef..))) (f482f.. (f482f.. (1670d.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. (1670d.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))).
Apply unknownprop_f927fc854d1321747373b1f08e7810d0d1c70d45322c996edf8ab8d4889debcc with
x1,
x2,
e3162.. (f482f.. (1670d.. x1 x2 x3 x4) (4ae4a.. 4a7ef..)),
x3,
f482f.. (f482f.. (1670d.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))),
x4,
decode_p (f482f.. (1670d.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) leaving 3 subgoals.
The subproof is completed by applying unknownprop_201c00f4dc546c1c361481e6df2db6a0eaaed987dfc99dd72aafe0c44e14d85c with x1, x2, x3, x4.
The subproof is completed by applying unknownprop_e22c9b8bbaf8c317cab2c404e4bfbf3bd3c6d0de5b90be91aa49bf9920fa5b22 with x1, x2, x3, x4.
Let x5 of type ι be given.
Apply unknownprop_ec7e3e177a83a4e42d38d8856b0fff216c61fbfa7dac384f7cc308a89915b411 with
x1,
x2,
x3,
x4,
x5,
λ x6 x7 : ο . iff (x4 x5) x6 leaving 2 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying iff_refl with x4 x5.