Let x0 of type ι be given.
Apply H0 with
λ x1 . x1 = 60b2c.. (f482f.. x1 4a7ef..) (e3162.. (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 → ι → ι be given.
Let x3 of type ι → ο be given.
Let x4 of type ι be given.
Apply unknownprop_848a12d392e8404e9fc3dd49be94ed27ceae23f19931a48e339b5aa92ae6295c with
x1,
x2,
x3,
x4,
λ x5 x6 . 60b2c.. x1 x2 x3 x4 = 60b2c.. x5 (e3162.. (f482f.. (60b2c.. x1 x2 x3 x4) (4ae4a.. 4a7ef..))) (decode_p (f482f.. (60b2c.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. (60b2c.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))).
Apply unknownprop_cdda72973dc0b5b6f0b46928fa4486ae7f28c61d3aa53ff1cbdff5c714bc6b4a with
x1,
x2,
x3,
x4,
λ x5 x6 . 60b2c.. x1 x2 x3 x4 = 60b2c.. x1 (e3162.. (f482f.. (60b2c.. x1 x2 x3 x4) (4ae4a.. 4a7ef..))) (decode_p (f482f.. (60b2c.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..)))) x5.
Apply unknownprop_2a58f9ed21aa9f96a2752499ff156a67ce26536a847ac82e578dee4e95e450ae with
x1,
x2,
e3162.. (f482f.. (60b2c.. x1 x2 x3 x4) (4ae4a.. 4a7ef..)),
x3,
decode_p (f482f.. (60b2c.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))),
x4 leaving 2 subgoals.
The subproof is completed by applying unknownprop_83df285a23471f1da5b54cf57ce9aa7010b1ec60eb9a7332adfdd0775116fcef with x1, x2, x3, x4.
Let x5 of type ι be given.
Apply unknownprop_92ebd3f7147f6de662aed94671adec8d6b4e8e50d19f8fe5ae090016dceb1248 with
x1,
x2,
x3,
x4,
x5,
λ x6 x7 : ο . iff (x3 x5) x6 leaving 2 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying iff_refl with x3 x5.