Let x0 of type ι be given.
Apply H0 with
λ x1 . x1 = 42836.. (f482f.. x1 4a7ef..) (2b2e3.. (f482f.. x1 (4ae4a.. 4a7ef..))) (decode_p (f482f.. x1 (4ae4a.. (4ae4a.. 4a7ef..)))).
Let x1 of type ι be given.
Let x2 of type ι → ι → ο be given.
Let x3 of type ι → ο be given.
Apply unknownprop_59ca09c0fd122f786673713c0642ed4ce1a31aabde53a2b0a8368edd8a739e79 with
x1,
x2,
x3,
λ x4 x5 . 42836.. x1 x2 x3 = 42836.. x4 (2b2e3.. (f482f.. (42836.. x1 x2 x3) (4ae4a.. 4a7ef..))) (decode_p (f482f.. (42836.. x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..)))).
Apply unknownprop_4529c7af96080e7b9afbea0a795b4cd504a4580e4c0eefff35ada6aa9e35d4a9 with
x1,
x2,
2b2e3.. (f482f.. (42836.. x1 x2 x3) (4ae4a.. 4a7ef..)),
x3,
decode_p (f482f.. (42836.. x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..))) leaving 2 subgoals.
Let x4 of type ι be given.
Let x5 of type ι be given.
Apply unknownprop_f9bb039047c575715dfc8b1b59b7b8ec67d811cbe7fb1bdb245069e08439d0a7 with
x1,
x2,
x3,
x4,
x5,
λ x6 x7 : ο . iff (x2 x4 x5) x6 leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying iff_refl with x2 x4 x5.
Let x4 of type ι be given.
Apply unknownprop_ccbf64b584877a997f6d8dee90614a29efc1b9f302b847ac9596ce2d25fc4cd2 with
x1,
x2,
x3,
x4,
λ x5 x6 : ο . iff (x3 x4) x5 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying iff_refl with x3 x4.