Let x0 of type ι be given.
Apply H0 with
λ x1 . x1 = 8f64a.. (f482f.. x1 4a7ef..) (e3162.. (f482f.. x1 (4ae4a.. 4a7ef..))) (e3162.. (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 → ι be given.
Let x4 of type ι → ο be given.
Apply unknownprop_36c42de3fa64ba0d931d2bce5c95c24271e7ca12e15351b214ce939787147f70 with
x1,
x2,
x3,
x4,
λ x5 x6 . 8f64a.. x1 x2 x3 x4 = 8f64a.. x5 (e3162.. (f482f.. (8f64a.. x1 x2 x3 x4) (4ae4a.. 4a7ef..))) (e3162.. (f482f.. (8f64a.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. (8f64a.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))).
Apply unknownprop_1c101b06aca859e9ba6f75c56a378d613efaee6c330ede5172ef21894198793e with
x1,
x2,
e3162.. (f482f.. (8f64a.. x1 x2 x3 x4) (4ae4a.. 4a7ef..)),
x3,
e3162.. (f482f.. (8f64a.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))),
x4,
decode_p (f482f.. (8f64a.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) leaving 3 subgoals.
The subproof is completed by applying unknownprop_4e842e2c30ccf0c3564e02682ecde09675764a8b5663da987f76b91e34225304 with x1, x2, x3, x4.
The subproof is completed by applying unknownprop_521087284df84a924fcf4bcd5859c5772f0f0c1ecfc3853224d5653fe7e0ef2c with x1, x2, x3, x4.
Let x5 of type ι be given.
Apply unknownprop_cd131d10c369b276d5ab02bbaa6503cd63c1cdda813ea32dfc1d611915267593 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.