Let x0 of type ι be given.
Apply H0 with
λ x1 . x1 = b5cc3.. (f482f.. x1 4a7ef..) (e3162.. (f482f.. x1 (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. x1 (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.
Apply unknownprop_2e4ad16a724aa9ecb1f2d0714afea104f57cf750321b796a86385476dc14b16d with
x1,
x2,
x3,
λ x4 x5 . b5cc3.. x1 x2 x3 = b5cc3.. x4 (e3162.. (f482f.. (b5cc3.. x1 x2 x3) (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. (b5cc3.. x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..)))).
Apply unknownprop_35925bfc248c62e0fad1bf3195f5286d826505ac11ea5d834c911ed7a4b878a2 with
x1,
x2,
e3162.. (f482f.. (b5cc3.. x1 x2 x3) (4ae4a.. 4a7ef..)),
x3,
2b2e3.. (f482f.. (b5cc3.. x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..))) leaving 2 subgoals.
The subproof is completed by applying unknownprop_15cd99d9ca461ad2237964118d360f2606f8cb1d2c65d040d581982ac836b5ae with x1, x2, x3.
Let x4 of type ι be given.
Let x5 of type ι be given.
Apply unknownprop_1b1870aad03d524430ecdbf45bff93c05749be68abe1a80eafa30ff7d1c8a1e5 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.