Let x0 of type ι be given.
Apply H0 with
λ x1 . x1 = 0fd05.. (f482f.. x1 4a7ef..) (e3162.. (f482f.. x1 (4ae4a.. 4a7ef..))) (2b2e3.. (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 → ο be given.
Let x4 of type ι → ο be given.
Apply unknownprop_b0f82d1c69f380550644ef11c2dd41f9d5d4f492a768abdd3d6e9adfd74b9c76 with
x1,
x2,
x3,
x4,
λ x5 x6 . 0fd05.. x1 x2 x3 x4 = 0fd05.. x5 (e3162.. (f482f.. (0fd05.. x1 x2 x3 x4) (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. (0fd05.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. (0fd05.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))).
Apply unknownprop_df43287c8d908363fca9e7f3c8cf211d70649e52421ddd3f09e67c8d5afd933d with
x1,
x2,
e3162.. (f482f.. (0fd05.. x1 x2 x3 x4) (4ae4a.. 4a7ef..)),
x3,
2b2e3.. (f482f.. (0fd05.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))),
x4,
decode_p (f482f.. (0fd05.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) leaving 3 subgoals.
The subproof is completed by applying unknownprop_fed6cf07aa814164a3daa084792cf9b08a4358b581f07c8eb65ac4ff36c71f64 with x1, x2, x3, x4.
Let x5 of type ι be given.
Let x6 of type ι be given.
Apply unknownprop_5ea683a46d4420d1129d98b68c2d8a411e60a35ab8618f29559598685876fec4 with
x1,
x2,
x3,
x4,
x5,
x6,
λ x7 x8 : ο . iff (x3 x5 x6) x7 leaving 3 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying iff_refl with x3 x5 x6.
Let x5 of type ι be given.
Apply unknownprop_47bb3b8d7a71a1e8960090c3da1b97fe4880f40eb7b56b3243c5a95be7978365 with
x1,
x2,
x3,
x4,
x5,
λ x6 x7 : ο . iff (x4 x5) x6 leaving 2 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying iff_refl with x4 x5.