Let x0 of type ι be given.
Apply H0 with
λ x1 . x1 = 73737.. (f482f.. x1 4a7ef..) (f482f.. (f482f.. x1 (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. x1 (4ae4a.. (4ae4a.. 4a7ef..)))).
Let x1 of type ι be given.
Let x2 of type ι → ι be given.
Let x3 of type ι → ι → ο be given.
Apply unknownprop_56fff63ae4aaffa24f98b7fb5e034afaf3bd48ea6cf337512ab94a8fb832e90d with
x1,
x2,
x3,
λ x4 x5 . 73737.. x1 x2 x3 = 73737.. x4 (f482f.. (f482f.. (73737.. x1 x2 x3) (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. (73737.. x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..)))).
Apply unknownprop_33f79147c8c618ce18e91cdf7d8f59f8f2bfecd58527518b49f7a21a644fdd5e with
x1,
x2,
f482f.. (f482f.. (73737.. x1 x2 x3) (4ae4a.. 4a7ef..)),
x3,
2b2e3.. (f482f.. (73737.. x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..))) leaving 2 subgoals.
The subproof is completed by applying unknownprop_0eba4a1e8a6eb85bd93458d64288a202dddf6558775b796d073829b1ed4aed10 with x1, x2, x3.
Let x4 of type ι be given.
Let x5 of type ι be given.
Apply unknownprop_d3745c59fd830feec1cf172211f6f2a659a425d7b1b42063659cffa5062c6422 with
x1,
x2,
x3,
x4,
x5,
λ x6 x7 : ο . iff (x3 x4 x5) x6 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 x4 x5.